Non-homogeneous objects magnification and reduction

CROSS-REFERENCES

0001The present invention relates to and claims priority from U.S. Provisional patent application No. 61/438,609, filed on Feb. 1, 2011, entitled ACTIVE AND SELECTED DOCUMENTS ON AXES THEREOF; EXPANDABLE AND COLLAPSIBLE AXES OF DOCUMENTS; NON-HOMOGENEOUS OBJECTS MAGNIFICATION AND REDUCTION, which is incorporated herein by reference.

FIELD OF THE INVENTION

0002This invention relates generally to computer systems and more specifically to a method, a system and an interface that facilitates the magnification and the reduction of objects on a display. More precisely, the present invention relates to a method of non-homogenously magnifying and reducing layouts of elements, objects and/or documents.

BACKGROUND OF THE INVENTION

0003Computers can come with a variety of display sizes. Desktop computers are adapted to be connected to large screen while mobile computers are required to deal with much smaller displays.

0004Magnifying information elements on a display generally requires magnification and reduction of the subject object displayed to maximize the use of the display area. Magnifying and reducing objects on a display equally magnifies intervening between-objects portions that do not need to be magnified because they do not add more meaning to the subject objects. Magnifying intervening between-objects portions use more display area that could be used more usefully by other objects.

0005Layout of objects can vary in accordance with a variety of possible uses. A problem arises with webpages, especially when seen on small screens like PDA's or mobile phones, which need to be magnified. Magnification of a webpage can be required for, for instance, becoming readable. Under some circumstances the magnification of the text is required for readability although the magnification of the margins around the text or enclosures in the text, like publicity or even images, might no be desirable considering the small size of the display area.

0006For instance, objects on a web page can include text and images that bring meaning to a reader. The text and the images are generally separated with margins thereof. Magnifying, for instance, a virtual newspaper to read it with, illustratively, a mobile phone, is going to also magnify the margins that are of no help for the reader since their smaller size, when they are not magnified, is sufficient to clearly distinguish the text from the images. In other words, their magnification is a non-optimal use of the display area that is available.

0007Similar principles can be applied to menu items using, for example, icons or the like in a predetermined graphical arrangements. Intervening margins between the menu items are magnified with the menu items and space is lost on the display area of the display while their enlargement (the margins) is of little help for the user since their smaller size was already sufficient to allow proper use of the menu items.

0008Today's information management systems are dealing with tremendous amounts of documents and other files. Files management systems are evolving toward a more graphical environment to facilitate document navigation and management. United States Patent Application Publication No.: US 2007/0214169 A1, published on Sep. 13, 2007 discloses a Multi-dimensional locating system and method (title). The patent application discloses ways for managing and displaying axes of documents and other computer-readable files. An axis of documents that groups a plurality of documents along a predetermined order, inter alia, is taught.

0009The use of only a small number of documents on a display might result in a poor use of the usable display area. A larger number of documents on an axis might be desirable. Similarly, a plurality of axes of documents might also be desirable to provide more information to a viewer. A number of challenges need to be addressed in order to provide some functions performed on a significant quantity of documents and/or a plurality of axes.

0010One of these challenges is to maximize the use of a display area when a number of documents on a single axis, or disposed on many axes displaying documents thereon, are simultaneously displayed. Magnifying (or reducing) the documents and/or the axes equally magnifies (or reduces) the margins around the documents and the axes. The magnification of the margins with the same magnification level for the documents and the axes might not be desirable. A small margin can be sufficient even with a strong magnification. The magnification of margins proportionally increases the non-useful area on the display.

0011In view of the prior art it appears that improvements over the prior art is desirable to improve the user experience and usability either with innovative graphical, structural or functional improvements.

SUMMARY OF THE INVENTION

0012The following presents a simplified summary of the invention in order to provide a basic understanding of some aspects of the invention. This summary is not an extensive overview of the invention. It is not intended to identify key/critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented later.

0013This invention generally refers to juxtaposed objects and intervening spaces thereof that do not require a similar magnification and/or reduction when they their size is changed. This invention also refers to user-selectable elements that might represent computer-readable files like documents and multimedia assets. Information elements can alternatively be referred to as, user-selectable elements, menu elements, icons or thumbnails that are associated to an attribute, a category or a tag and arranged as explained below. In order to lighten the reading of the present specification, the term “document” is generally used without intending to limit the scope of the present patent application only to documents, unless expressly specified.

0014Also, the invention is generally described using an assembly of documents called an axis of documents. The axis of documents generally refers to, but is not limited to, a comprehensive graphical layout of documents. Hereinbelow referred to as an axis that is embodied as a substantially rectilinear arrangement of documents. The axis might not necessarily be straight but preferably has a consistent shape providing a viewer an indication of continuity therebetween documents disposed thereon. In other words, the axis of documents can be defined by a single axis, a double axis of documents, or more adjacent axes of documents. The axis can be completely straight, slightly curved, substantially curved, angled, following a particular shape or having a consistent shape over which documents are disposed in a reasonably consistent fashion adapted to allow a viewer to infer a comprehensive suite of documents. The axes presented in the embodiments below are illustrated in the horizontal position while they could be disposed vertically without departing from the scope of the present disclosure.

0015An embodiment referred to below provides one or more groups of axes comprising documents thereon. Each axis of documents is preferably rectilinear to easily be located adjacent with other axes of documents to efficiently use the useful display area of the display. A system adapted to carry on the embodiments, a user graphical interface adapted to display the embodiments, a method adapted to provides the steps required to enable the embodiments and a medium storing instructions enabling the method once read by a machine are all considered within the scope of the present invention.

0016The present patent specification refers most of the time to a magnification function and a reduction function to lighten readability of the text. Whenever the function magnification is referred to alone, it also implicitly refers to its opposite and complementary function: the reduction.

0017An embodiment referred to below provides a means for magnifying and/or reducing meaningful objects on a display without magnifying and/or reducing intervening spaces and unmeaningful objects on a display to maximize the use of the useful viewing area of the display in at least an embodiment of the present invention.

0018An embodiment referred to below provides at least a mechanism, a method, an apparatus, a system and/or a graphical user interface adapted to non-homogeneously magnify and/or reduce a visible area of a display in at least an embodiment of the present invention.

0019An embodiment referred to below provides a mechanism configured to magnify and/or reduce some displayed objects while not magnify and/or reduce some other simultaneously displayed objects in at least an embodiment of the present invention.

0020An embodiment referred to below provides a method of determining which objects on a display are adapted to be magnified and/or reduced and which objects, intervening spaces and/or margins are not adapted to be magnified and/or reduced in at least an embodiment of the present invention.

0021An embodiment referred to below provides a method of grouping objects adapted to be displayed on a display that are adapted to be magnified and/or reduced and objects, intervening spaces and/or margins are not adapted to be magnified and/or reduced, to be used by a computer system to batch manage magnification and/or reduction of objects in at least an embodiment of the present invention.

0022An embodiment referred to below provides a mechanism configured to magnify and/or reduce some displayed objects at a defined rate while not magnify and/or reduce some other simultaneously displayed objects at the same rate; the magnify and/or reduce rates being linear or non-linear in at least an embodiment of the present invention.

0023An embodiment referred to below provides a method, a system and a graphical user interface configured to magnify and/or reduce only specific objects among a larger group of objects in at least an embodiment of the present invention.

0024An embodiment referred to below provides a magnification and/or reduction of one of many objects without magnification and/or reducing environment structures in at least an embodiment of the present invention.

0025An embodiment referred to below provides a method of magnification and/or reducing a layout of objects by magnifying the objects at a first magnifying rate and the surrounding environment at a second magnifying rate in at least an embodiment of the present invention.

0026An embodiment referred to below provides a first object magnification and/or reduction rate between a first size and a second size, and a second object magnification and/or reduction rate between the second size and a third size and also a first margin magnification and/or reduction rate between a first size and a second size and a second magnification and/or reduction rate between the second size and a third size in at least an embodiment of the present invention.

0027An embodiment referred to below provides a magnification and/or reduction anchor adapted to set the position of a layout of objects that is going to remain at the same place on a display during magnification and/or reduction in at least an embodiment of the present invention.

0028An embodiment referred to below provides a method of magnifying and or reducing documents in a layout of documents defining borders and margins by magnifying and/or reducing the documents and not magnifying and/or reducing the surrounding environment, the borders and/or the margins in at least an embodiment of the present invention.

0029An embodiment referred to below provides a method of magnifying documents in a layout of documents defining borders and margins by magnifying the documents and not magnifying the borders and the margins in at least an embodiment of the present invention.

0030An embodiment referred to below provides a product comprising a machine-readable medium; and machine-executable instructions for causing a computer to perform a method comprising providing a first object and a second object at least partially graphically circumventing the first object, the first object and the second object being adapted to be simultaneously displayed on a display area of a display; non-homogeneously changing a size of the two objects.

0031An embodiment referred to below provides a method of magnifying an array of information elements on a display, the method comprising displaying a plurality of information elements on the display with a size thereof, at least some of the plurality of information elements being surrounded by a margin thereof, and modifying the size of the plurality of displayed information elements on a basis of a first magnitude, at least a portion of the margins being adapted to change size on a basis of a second magnitude thereof.

0032An embodiment referred to below provides a method of non-homogeneously magnifying objects on a display, the method comprising providing an information element adapted to be displayed on a display and surrounded by a margin thereof; displaying the information element and its margin on a display; defining a standardized object adapted to respectively include therein the information element and at least a portion of the margin; magnifying the standardized object; defining a size of the magnified information element by removing an unmagnified size of the at least a potion of the margin to the size of the magnified standardized object; and displaying the magnified information element with its surrounding margin.

0033Other advantages might become apparent to the skilled reader of this patent specification in light of the text and appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

0034<figref idref="DRAWINGS">FIG. 1</figref> is a schematic illustration of an exemplary computerized network;

0035<figref idref="DRAWINGS">FIG. 2</figref> is a schematic illustration of an exemplary multi-devices network layout;

0036<figref idref="DRAWINGS">FIG. 3</figref> is a schematic illustration of a typical exemplary computer system;

0037<figref idref="DRAWINGS">FIG. 4</figref> is a schematic illustration of a prior art axis of documents in a longitudinal arrangements of documents;

0038<figref idref="DRAWINGS">FIG. 5</figref> is a schematic illustration of a magnified portion of the axis of documents of <figref idref="DRAWINGS">FIG. 4</figref>;

0039<figref idref="DRAWINGS">FIG. 6</figref> is a schematic illustration of an axis of documents in a zoomed out configuration with fixed intervening portions in accordance with an embodiment of the present invention;

0040<figref idref="DRAWINGS">FIG. 7</figref> is a schematic illustration of an axis of documents in a zoomed in configuration with fixed intervening portions in accordance with an embodiment of the present invention;

0041<figref idref="DRAWINGS">FIG. 8</figref> is a schematic illustration of an axis of documents in a strong zoomed in configuration with fixed intervening portions in accordance with an embodiment of the present invention;

0042<figref idref="DRAWINGS">FIG. 9</figref> is an illustrative schematic view of the relative position of schematic layout of documents in accordance with an embodiment of the present invention;

0043<figref idref="DRAWINGS">FIG. 10</figref> is an illustrative schematic view of the relative position of a magnified schematic layout of documents in accordance with an embodiment of the present invention;

0044<figref idref="DRAWINGS">FIG. 11</figref> is an illustrative schematic view of the relative position of schematic layout of documents in accordance with an embodiment of the present invention;

0045<figref idref="DRAWINGS">FIG. 12</figref> is an illustrative schematic view of the relative position of a magnified schematic layout of documents in accordance with an embodiment of the present invention;

0046<figref idref="DRAWINGS">FIG. 13</figref> is an illustrative schematic view of an axis of documents in accordance with an embodiment of the present invention;

0047<figref idref="DRAWINGS">FIG. 14</figref> is an illustrative schematic view of the intervening portions around each document in accordance with an embodiment of the present invention;

0048<figref idref="DRAWINGS">FIG. 15</figref> is an illustrative schematic view of the axis of document and their intervening portions considered as a single object in accordance with an embodiment of the present invention;

0049<figref idref="DRAWINGS">FIG. 16</figref> is an illustrative schematic view of multiple axes of objects without intervening portions in accordance with an embodiment of the present invention;

0050<figref idref="DRAWINGS">FIG. 17</figref> is an illustrative schematic view of the magnification of multiple axes of objects without intervening portions in accordance with an embodiment of the present invention;

0051<figref idref="DRAWINGS">FIG. 18</figref> is an illustrative schematic view of the magnification of multiple axes of objects without intervening portions in accordance with an embodiment of the present invention;

0052<figref idref="DRAWINGS">FIG. 19</figref> is an illustrative schematic view of the representation of the different components of a document and its intervening portions as a object in accordance with the embodiment of the present invention;

0053<figref idref="DRAWINGS">FIG. 20</figref> is an illustrative schematic view of a group of axes of documents with intervening portions, margins and headers in accordance with an embodiment of the present invention;

0054<figref idref="DRAWINGS">FIG. 21</figref> is an illustrative schematic view of a magnified group of axes of documents with fixed intervening portions, margins and headers in accordance with an embodiment of the present invention;

0055<figref idref="DRAWINGS">FIG. 22</figref> is an illustrative schematic view of a magnified group of axes of documents with fixed intervening portions, margins and headers axis names in accordance with an embodiment of the present invention;

0056<figref idref="DRAWINGS">FIG. 23</figref> is an illustrative schematic view of a group of axes of documents with a fixed size intervening portions and/or header in accordance with an embodiment of the present invention.

0057<figref idref="DRAWINGS">FIG. 24</figref> is an illustrative schematic view of a magnified group of axes of documents with a fixed size intervening portions and/or header in accordance with an embodiment of the present invention.

0058<figref idref="DRAWINGS">FIG. 25</figref> is an illustrative schematic view of a magnified group of axes of documents with a fixed size intervening portions and/or header in accordance with an embodiment of the present invention.

0059<figref idref="DRAWINGS">FIG. 26</figref> is an illustrative schematic view of a group of axes of documents with a magnifiable size intervening portions and/or header and visual distinctive features applied to some document in accordance with an embodiment of the present invention;

0060<figref idref="DRAWINGS">FIG. 27</figref> is an illustrative schematic view of a group of axes of documents with a magnifiable size intervening portions and/or header and visual distinctive features applied to some document in accordance with an embodiment of the present invention;

0061<figref idref="DRAWINGS">FIG. 28</figref> is an illustrative schematic view of a group of axes of documents with a magnifiable size intervening portions and/or header and visual distinctive features applied to some document in accordance with an embodiment of the present invention;

0062<figref idref="DRAWINGS">FIG. 29</figref> is an illustrative schematic view of plurality of axes of documents with two marking axes in accordance with an embodiment of the present invention;

0063<figref idref="DRAWINGS">FIG. 30</figref> is an illustrative schematic view of plurality of magnified axes of documents with two marking axes in accordance with an embodiment of the present invention;

0064<figref idref="DRAWINGS">FIG. 31</figref> is an illustrative schematic view of plurality of magnified axes of documents in a display area with two marking axes in accordance with an embodiment of the present invention;

0065<figref idref="DRAWINGS">FIG. 32</figref> is an illustrative schematic view of a group of axes of square documents in accordance with an embodiment of the present invention;

0066<figref idref="DRAWINGS">FIG. 33</figref> is an illustrative schematic view of a group of axes of rectangular documents in accordance with an embodiment of the present invention;

0067<figref idref="DRAWINGS">FIG. 34</figref> is an illustrative schematic view of a group of axes of rectangular documents in accordance with an embodiment of the present invention;

0068<figref idref="DRAWINGS">FIG. 35</figref> is an illustrative schematic view of a group of axes of square documents in accordance with an embodiment of the present invention;

0069<figref idref="DRAWINGS">FIG. 36</figref> is an schematic illustration of several shapes adapted to be maximized in document containers in accordance with an embodiment of the present invention;

0070<figref idref="DRAWINGS">FIG. 37</figref> is an schematic illustration of several shapes maximized in magnified document containers in accordance with an embodiment of the present invention;

0071<figref idref="DRAWINGS">FIG. 38</figref> is an illustrative schematic view of a group of axes of documents of equals dimension in accordance with an embodiment of the present invention;

0072<figref idref="DRAWINGS">FIG. 39</figref> is an illustrative schematic view of a group of a plurality of axes of documents in which one axis of documents is being reduced in accordance with an embodiment of the present invention;

0073<figref idref="DRAWINGS">FIG. 40</figref> is an illustrative schematic view of a plurality of axes of documents and a non-parallel axis of documents over one element of an axis of documents in accordance with an embodiment of the present invention;

0074<figref idref="DRAWINGS">FIG. 41</figref> is an illustrative schematic view of a plurality of magnified axes of documents and a non-parallel axis of documents over one document of another axis of documents in accordance with an embodiment of the present invention;

0075<figref idref="DRAWINGS">FIG. 42</figref> is a schematic illustration of a web document with fixed intervening portions in accordance with an embodiment of the present invention; and

0076<figref idref="DRAWINGS">FIG. 43</figref> is a schematic illustration of a magnified web page with fixed intervening portions in accordance with an embodiment of the present invention.

DESCRIPTION OF EMBODIMENT(S) OF THE INVENTION

0077The present invention is now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It may be evident, however, that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate describing the present invention.

0078The description is separated with subtitles to facilitate its readability. The subtitles include descriptions of portions of invention that might be interrelated despite they might appear under different subtitles. In other words, subtitles are not intended to separate part of the same invention or different inventions described therein but are rather intended to structure the text.

0079The features provided in this specification mainly relates to basic principles for managing axes of documents. These code/instructions are preferably stored on a machine-readable medium adapted to be read and acted upon to with a computer or a machine having corresponding code/instructions reading capability.

0080Exemplary Network

0081<figref idref="DRAWINGS">FIG. 1</figref> illustrates an exemplary network <b>10</b> in which a system and method, consistent with the present invention, may be implemented. The network <b>10</b> may include multiple client devices <b>12</b> connected to multiple servers <b>14</b>, <b>16</b>, <b>18</b> via a network <b>20</b>. The network <b>20</b> may include a local area network (LAN), a wide area network (WAN), a telephone network, such as the Public Switched Telephone Network (PSTN), an intranet, the Internet, Wi-Fi, WiMAX or a combination of networks. Two client devices <b>12</b> and three servers <b>14</b>, <b>16</b>, <b>18</b> have been illustrated as connected to network <b>20</b> for simplicity. In practice, there may be more or less client devices and servers. Also, in some instances, a client device may perform the functions of a server and a server may perform the functions of a client device.

0082The client devices <b>12</b> may include devices, such as mainframes, minicomputers, personal computers, laptops, personal digital assistants, telephones, or the like, capable of connecting to the network <b>20</b>. The client devices <b>12</b> may transmit data over the network <b>20</b> or receive data from the network <b>20</b> via a wired, wireless, or optical connection.

0083The servers <b>14</b>, <b>16</b>, <b>18</b> may include one or more types of computer systems, such as a mainframe, minicomputer, or personal computer, capable of connecting to the network <b>20</b> to enable servers <b>14</b>, <b>16</b>, <b>18</b> to communicate with the client devices <b>12</b>. In alternative implementations, the servers <b>14</b>, <b>16</b>, <b>18</b> may include mechanisms for directly connecting to one or more client devices <b>12</b>. The servers <b>14</b>, <b>16</b>, <b>18</b> may transmit data over network <b>14</b> or receive data from the network <b>20</b> via a wired, wireless, or optical connection.

0084In an implementation consistent with the present invention, the server <b>14</b> may include a search engine <b>22</b> usable by the client devices <b>12</b>. The servers <b>14</b> may store documents, such as web pages, accessible by the client devices <b>12</b>.

0085With reference to <figref idref="DRAWINGS">FIG. 2</figref>, a network <b>20</b> includes the content cloud <b>30</b>, a content database <b>32</b>, content devices <b>34</b>-<b>38</b>, and devices <b>40</b>-<b>48</b>. The network mediator <b>28</b> enables the network devices <b>32</b>-<b>38</b> to communicate with each other without pre-configuring each device.

0086The content cloud <b>30</b> represent a content source such as the Internet, where content exists at various locations across the globe. The content includes multimedia content such as audio and video. The mediator <b>28</b> allows the content cloud to provide content to devices <b>40</b>-<b>48</b>.

0087The content database <b>32</b> is a storage device that maintains content. The content database <b>32</b> may be a stand-alone device on an external communication network. The mediator <b>28</b> communicates with the content database <b>32</b> to access and retrieve content.

0088The content devices <b>34</b>-<b>38</b> include intelligent devices, such as, for example, personal computers, laptops, cell phones and personal digital assistants. The content devices <b>32</b>-<b>38</b> are capable or storing content information.

0089The devices <b>40</b>-<b>48</b> are intelligent devices that receive content from a content source <b>30</b>-<b>38</b>. However, the devices <b>30</b>-<b>38</b> can also operate as servers to distribute content to other client devices.

0090Exemplary Client Architecture

0091<figref idref="DRAWINGS">FIG. 3</figref> and the following discussion provide a brief, general description of an exemplary apparatus in which at least some aspects of the present invention may be implemented. The present invention will be described in the general context of computer-executable instructions, such as program modules, being executed by a personal computer. However, the methods of the present invention may be effected by other apparatus. Program modules may include routines, programs, objects, components, data structures, applets, WEB 2.0 type of evolved networked centered applications, etc. that perform a task(s) or implement particular abstract data types. Moreover, those skilled in the art will appreciate that at least some aspects of the present invention may be practiced with other configurations, including hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network computers, minicomputers, set top boxes, mainframe computers, gaming console and the like. At least some aspects of the present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. In a distributed computing environment, program modules may be located in local and/or remote memory storage devices.

0092Now, with reference to <figref idref="DRAWINGS">FIG. 3</figref>, an exemplary apparatus <b>100</b> for implementing at least some aspects of the present invention includes a general purpose computing device in the form of a conventional personal computer <b>120</b>. The personal computer <b>120</b> may include a processing unit <b>121</b>, a system memory <b>122</b>, and a system bus <b>123</b> that couples various system components, including the system memory <b>122</b>, to the processing unit <b>121</b>. The system bus <b>123</b> may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The system memory may include read only memory (ROM) <b>124</b> and/or random access memory (RAM) <b>125</b>. A basic input/output system <b>126</b> (BIOS), containing basic routines that help to transfer information between elements within the personal computer <b>120</b>, such as during start-up, may be stored in ROM <b>124</b>. The personal computer <b>120</b> may also include a hard disk drive <b>127</b> for reading from and writing to a hard disk, (not shown), a magnetic disk drive <b>128</b> for reading from or writing to a (e.g., removable) magnetic disk <b>129</b>, and an optical disk drive <b>130</b> for reading from or writing to a removable (magneto) optical disk <b>131</b> such as a compact disk or other (magneto) optical media. The hard disk drive <b>127</b>, magnetic disk drive <b>128</b>, and (magneto) optical disk drive <b>130</b> may be coupled with the system bus <b>123</b> by a hard disk drive interface <b>132</b>, a magnetic disk drive interface <b>133</b>, and a (magneto) optical drive interface <b>134</b>, respectively. The drives and their associated storage media provide nonvolatile (or persistent) storage of machine-readable instructions, data structures, program modules and other data for the personal computer <b>120</b>. Although the exemplary environment described herein employs a hard disk, a removable magnetic disk <b>129</b> and a removable optical disk <b>131</b>, those skilled in the art will appreciate that other types of storage media, such as magnetic cassettes, flash memory cards, digital video disks, Bernoulli cartridges, random access memories (RAMs), read only memories (ROM), and the like, may be used instead of, or in addition to, the storage devices introduced above.

0093A number of program modules may be stored on the hard disk <b>127</b>, magnetic disk <b>129</b>, (magneto) optical disk <b>131</b>, ROM <b>124</b> or RAM <b>125</b>, such as an operating system <b>135</b> (for example, Windows® NT.® 4.0, sold by Microsoft® Corporation of Redmond, Wash.), one or more application programs <b>136</b>, other program modules <b>137</b> (such as “Alice”, which is a research system developed by the User Interface Group at Carnegie Mellon University available at www.Alice.org, OpenGL from Silicon Graphics Inc. of Mountain View Calif., or Direct 3D from Microsoft Corp. of Bellevue Wash.), and/or program data <b>138</b> for example.

0094A user may enter commands and information into the personal computer <b>120</b> through input devices, such as a keyboard <b>140</b>, a camera <b>141</b> and pointing device <b>142</b> for example. Other input devices (not shown) such as a microphone, joystick, game pad, satellite dish, scanner, a touch sensitive screen, accelerometers adapted to sense movements of the user or movements of a device, or the like may also be included. These and other input devices are often connected to the processing unit <b>121</b> through a serial port interface <b>146</b> coupled to the system bus. However, input devices may be connected by other interfaces, such as a parallel port, a game port, blue tooth connection or a universal serial bus (USB). For example, since the bandwidth of the camera <b>141</b> may be too great for the serial port, the video camera <b>141</b> may be coupled with the system bus <b>123</b> via a video capture card (not shown). The video monitor <b>147</b> or other type of display device may also be connected to the system bus <b>123</b> via an interface, such as a video adapter <b>148</b> for example. The video adapter <b>148</b> may include a graphics accelerator. One or more speaker <b>162</b> may be connected to the system bus <b>123</b> via a sound card <b>161</b> (e.g., a wave table synthesizer such as product number AWE64 Gold Card from Creative® Labs of Milpitas, Calif.). In addition to the monitor <b>147</b> and speaker(s) <b>162</b>, the personal computer <b>120</b> may include other peripheral output devices (not shown), such as a printer for example. As an alternative or an addition to the video monitor <b>147</b>, a stereo video output device, such as a head mounted display or LCD shutter glasses for example, could be used.

0095The personal computer <b>120</b> may operate in a networked environment that defines logical connections to one or more remote computers, such as a remote computer <b>149</b>. The remote computer <b>149</b> may be another personal computer, a server, a router, a network PC, a peer device or other common network node, and may include many or all of the elements described above relative to the personal computer <b>120</b>, although only a memory storage device has been illustrated in <figref idref="DRAWINGS">FIG. 1</figref>. The logical connections depicted in <figref idref="DRAWINGS">FIG. 2</figref> include a local area network (LAN) <b>14</b> and a wide area network (WAN) <b>152</b>, an intranet and the Internet.

0096When used in a LAN, the personal computer <b>120</b> may be connected to the LAN <b>14</b> through a network interface adapter (or “NIC”) <b>153</b>. When used in a WAN, such as the Internet, the personal computer <b>120</b> may include a modem <b>154</b> or other means for establishing communications over the wide area network <b>152</b> (e.g. Wi-Fi, WiMax . . . ). The modem <b>154</b>, which may be internal or external, may be connected to the system bus <b>123</b> via the serial port interface <b>146</b>. In a networked environment, at least some of the program modules depicted relative to the personal computer <b>120</b> may be stored in the remote memory storage device. The network connections shown are exemplary and other means of establishing a communications link between the computers may be used.

0097The Interface

0098An interface program providing an interface for managing documents in accordance with an embodiment of the invention is installed on a machine e.g. a computer system. The interface can be programmed using various programming languages e.g. C++, Java or other suitable programming languages. Programming of these languages is well known in the art and is adapted to be readable to provide executable instructions to a hardware system and will not be further described therein. The interface might run through the operating system and the hardware of the computer system or, alternatively, through a network based system e.g. client-server, and/cloud computing system. The interface is adapted to manage documents, computer files, pictures, multimedia content, applications (i.e. computer programs), menu elements, sets of icons and other user-selectable elements in a comprehensive fashion.

0099Several embodiments follows: Documents are stored on a machine-readable medium and can be retrieved on demand when needed with the interface program. Documents are disposed in an axis-like layout providing a visually comprehensive display arrangement of the documents. The axis can, illustratively, among other possibilities, be based on a selection of attribute(s), tag(s), category(ies), owner of documents, a chronological order, a statistical order or an order representing an increasing file size. Combinations of the above-listed possible choices, inter alia, are possible if desired to build a query adapted to reduce the number of documents to be displayed on the axis. The axis thus helps the viewer to infer additional meaning from the comprehensive layout, consistent display and distribution of the documents thereon.

0100An axis is adapted to accommodate a single type of documents or, if desired, more than one type of documents, and/or a mix of documents, computer files, multimedia contents and/or user-selectable menu elements. Documents might overlap to squeeze more documents on the space available on the display. Magnification of selected documents on an axis can be made to increase the level of details of the selected documents.

0101Using an axis of documents helps to meaningfully and intuitively display a group of documents. An axis of documents can be embodied as being a substantially linear distribution of documents adapted to dispose each document to be displayed on a line or on a curved line. A curved or a circular axis of documents is also contemplated to be within the scope of the present disclosure. The exact shape of the axis is secondary, what matters, inter alia, is that the layout structure of an axis provides a comprehensive suite of documents from which a viewer can infer an order, a sequence or a relationship between documents. The display of the axis of documents might be made in accordance with a predetermined order (e.g. chronologically), or not. A chronological distribution of documents can sort documents on a timeline. The chronological order can either be linear or non-linear; meaning that a unit of time has always the same graphical length on the display in the linear configuration. The non-linear configuration might non-evenly display similar units of time because the distribution of documents along the timeline prevails over the linearity of time. Another illustrative embodiment is a group of juxtaposed axes of documents grouped together to form an axis of documents referring to a matrix of documents.

0102The display of documents on an axis of documents allows to contextually manage documents as a flow, or an ongoing suite, of documents instead of dealing with each document independently. By getting away from managing each document independently it becomes possible to efficiently deal with a significantly higher number of documents and still keep the documents in a structured order.

0103Each axis of documents groups documents in accordance with, for example, a selected tag, a category, keywords, or an attribute that is commonly shared among the documents displayed on the axis of documents. The term “attribute” will consistently be used throughout the instant specification to lighten the reading of the text and will include the other commonality between documents described therein unless otherwise specified. The selection of one or more attribute (using Boolean logic for instant) determines which documents will be displayed on the axis of documents. If no specific attribute is selected, then, the axis of documents displays all documents. Thus, all documents on the same axis of documents are normally associated with the selected set or combination of attributes (trivial data, like publicity or specific related information, could be added to an axis as long as the outcome remains a presentation of documents resulting from a query without departing from the scope of the present invention). In addition, a timeline can be used to determine the order of the suite of documents on the axis of documents. Chronological ordering is a very intuitive ordering to humans and is one of the preferred ways to present documents on an axis of documents. In the case of a matrix of documents, then, one axis (e.g. horizontal direction) of the matrix can represent a timeline while the other axis (e.g. vertical direction, orthogonal, . . . ) represents another criterion like, for example, the type of computer files each document relates to. The other axis can also use a timeline if desirable.

0104The attributes of a document can be selected to create another axis of documents. The attribute of a document from the newly created axis of documents can be selected to create an additional axis of documents and so on so forth. This is what could be called “relational navigation” and is well described in the United States patent application publication referred to at the beginning of the present patent specification. Hence, the user can “navigate” along axes of documents in accordance with their categorization to visualize the documents. Navigation tools are provided with the interface to allow navigation through various axes of documents, when a plurality of axes is enabled, and through the documents of a single axis of documents. In the context of the present invention, a single suite of documents forming an axis along a timeline is one of the preferred embodiments because it is easy to sequentially navigate throughout the documents disposed along the axis. Other graphical layouts of documents might become obvious for a skilled reader in light of the present application and would be considered within the scope of this application.

0105When only a portion of the axis is visible, a play of zoom, pan and movements along the axis allows a viewer to navigate on the axis and change the document(s) that is(are) displayed on the display. A small display area could display only one document from the axis of documents while the remaining documents from the axis of documents are not displayed but remain nonetheless at their respective “virtual” position on the axis and ready to be displayed if the axis is scrolled to show other documents. In other words, if we consider a mobile platform like a mobile phone having a small display, the small display area might allow to efficiently display only one document at the time. However, the displayed document being part of an axis of documents, the other documents on the axis of documents remain displayable in accordance with their respective position on the axis of documents when the axis is scrolled/navigated/gestured.

0106Referring now to <figref idref="DRAWINGS">FIG. 4</figref>, it is possible to appreciate a plurality of documents <b>200</b> disposed on an axis of documents <b>210</b>. Each document <b>200</b> is located on axis of documents <b>210</b> that is illustratively defined by borders or rails <b>215</b>. The documents <b>200</b> are vertically located between rails <b>215</b> with a margin <b>220</b> above and another margin below. The documents <b>200</b> are separated apart from adjacent documents <b>200</b> with an intervening margin <b>225</b>.

0107A magnification of the axis of documents <b>210</b> of <figref idref="DRAWINGS">FIG. 4</figref> leads to a proportional magnification of all components (or objects). As illustrated in magnified <figref idref="DRAWINGS">FIG. 5</figref>, the documents <b>200</b> and the margins <b>220</b>, <b>225</b> are bigger but all proportions have been kept unchanged from the original size illustrated in <figref idref="DRAWINGS">FIG. 4</figref>. One can appreciate that the documents <b>200</b> are larger and easier to read but the margins <b>220</b>, <b>225</b> are also substantially larger and do not necessarily provide additional advantages to the viewer. In fact, in the case that the axis of documents <b>210</b> is displayed on a small display like a mobile phone, the expansion of the margins <b>220</b>, <b>225</b> take some valuable viewing area from the display, which is mostly undesirable.

0108An embodiment of the present invention provides an improved way to magnify/reduce a layout of documents <b>200</b> (on an axis <b>215</b> or not) by setting the size of the margins <b>220</b>, <b>225</b> such that they do not change in size with the documents <b>200</b> (or other objects).

0109An alternate embodiment suggests that the margins <b>220</b>, <b>225</b> do not magnify and/or reduce proportionally with the magnification and/or reduction of the documents <b>200</b>. For instance, the margins <b>220</b>, <b>225</b> can remain fixed for a change in size of the documents when the documents are of significant sizes. However, when the documents are rather small and are further magnified, the impact of the magnified margins <b>220</b>, <b>225</b> is more significant on the viewing area of the display. This is why one embodiment of the invention provides a non-linear relation between the magnification of the documents and the change in size of the margins <b>220</b>, <b>225</b>. The margins <b>220</b>, <b>225</b> can remain fixed over a portion of the possible documents size variation while it changes over a different portion of the documents size variation. Preferably, as mentioned above, it might be desirable to change the proportions of the margins <b>220</b>, <b>225</b> when the documents are very small.

0110Referring to <figref idref="DRAWINGS">FIGS. 6 through 8</figref>, an axis of documents <b>210</b> is shown in three different sizes. However, this time, the margins <b>220</b>, <b>225</b> remain fixed and are not magnified with the documents <b>200</b>. It can be appreciated from <figref idref="DRAWINGS">FIGS. 6 through 8</figref> the emphasis is put on the documents <b>200</b> while the margins <b>220</b>, <b>225</b> remains as proper separations to help distinguish and graphically distance the documents <b>200</b> from one another. In this embodiment, the fact that the margins <b>220</b>, <b>225</b> are not magnified does not harm the perception of separation between the documents <b>200</b> and the margins <b>220</b>, <b>225</b> do not take unnecessary space on the useful viewing area of a display (the display is not illustrated on the Figures, it is assumed that a skilled reader in the art of document management systems and interfaces thereof is going to understand that the embodiments depicted in the Figures are intended to represent displayed objects on a display or a portion thereof without being confused).

0111<figref idref="DRAWINGS">FIG. 9</figref> and <figref idref="DRAWINGS">FIG. 10</figref> illustrate two adjacent schematic axes of documents <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b>. Their respective relative positions are material for a user to obtain a consistent and comprehensive graphical representation thereof to ensure that a viewer would not be confused when they are both magnified. Now, lets take document <b>200</b>.<b>6</b> in axis of documents <b>210</b>.<b>1</b> in relation with document <b>200</b>.<b>4</b> in axis of documents <b>210</b>.<b>2</b> illustrated by line <b>230</b>. It is clear that line <b>230</b> falls between document <b>200</b>.<b>4</b> and <b>200</b>.<b>5</b> of axis of documents <b>210</b>.<b>2</b> in <figref idref="DRAWINGS">FIG. 9</figref>. After a magnification doubling the sizes of documents from <figref idref="DRAWINGS">FIG. 9</figref> to <figref idref="DRAWINGS">FIG. 10</figref>, while keeping margins thereof unmagnified, the same line <b>230</b>, now identified as line <b>230</b>.<b>2</b> is drawn on document <b>200</b>.<b>4</b> from axis of documents <b>210</b>.<b>2</b>. The difference between the position of line <b>230</b> before magnification, illustrated with dotted line <b>230</b>.<b>1</b> in <figref idref="DRAWINGS">FIG. 10</figref>, and the position of line <b>230</b>, from <figref idref="DRAWINGS">FIG. 9</figref>, after magnification, now line <b>230</b>.<b>2</b>, is illustrated with arrows <b>235</b>.

0112This means that there is a relative longitudinal displacement between documents <b>200</b> disposed along two (or more) axes of documents <b>210</b> if the margins are not magnified linearly with the documents. In other words, if the complete image is not magnified as a whole, a misalignment is created between juxtaposed axes of documents <b>210</b> as it is exemplified in <figref idref="DRAWINGS">FIG. 9</figref> and <figref idref="DRAWINGS">FIG. 10</figref>. A mathematical proof of this misalignment reads as follow in Equation 1: The two axes of documents <b>210</b>.<b>1</b>, <b>210</b>.<b>2</b> are disposed next to each other with an intervening space of an arbitrary size. The first axis of documents <b>210</b>.<b>1</b> has five documents <b>200</b>, when taken from the left, to line <b>230</b>. A document <b>200</b> has, for example, a size of one (1) unit and intervening margins of a size of one (1) unit, the sum is 10, as seen in equation 1a). The second axis of document have four documents of a size of two (2) units and intervening margins of a size of one (1) unit, the sum is 10 as seen in equation 1b). These two axes of documents are well aligned. After magnification of the axes of documents <b>210</b> by a factor of two (2), as it is illustrated in <figref idref="DRAWINGS">FIG. 10</figref>, the sum of the first axis of documents <b>210</b>.<b>1</b> is 15, as depicted in equation 1c), and the second axis of documents has a sum of 16, as identified in equation 1d). The sums of the two magnified axes of documents <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b> illustrated in <figref idref="DRAWINGS">FIG. 10</figref> are not equal anymore as it was with the Equations 1a) and 1b) referring to <figref idref="DRAWINGS">FIG. 9</figref>. The difference in the sum is the discrepancy generated by the magnification. The two equations 1c) and 1d) should be equals if the magnification of juxtaposed axes of documents <b>210</b> could keep the same alignment.

0000<br />5·1+5=10  a)

0000<br />4·1.5+4=10  b)

0000<br />5·2+5=15  c)

0000<br />4·3+4=16  d)

0113Equation 1

0114A similar example of misalignment is illustrated in <figref idref="DRAWINGS">FIG. 11</figref> and <figref idref="DRAWINGS">FIG. 12</figref> using axes of documents <b>210</b> and documents <b>200</b>. Again, the difference between the position of line <b>230</b> before magnification, illustrated with dotted line <b>230</b>.<b>1</b>, and the position of line <b>230</b> after a factor two (2) magnification with fixed margins, now line <b>230</b>.<b>2</b>, is illustrated with arrow <b>235</b>. One can appreciate that the difference is substantial. Another line <b>240</b> associated to document <b>200</b>.<b>2</b> from axis of documents <b>210</b>.<b>1</b> is illustrated in <figref idref="DRAWINGS">FIG. 11</figref> and <figref idref="DRAWINGS">FIG. 12</figref> to show that even after a short length on an axis of documents <b>210</b> (in the present situation after only two documents) there is a substantial difference between two juxtaposed axes of documents <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b>.

0115Moving now to <figref idref="DRAWINGS">FIG. 13</figref> that is virtually similar to <figref idref="DRAWINGS">FIG. 4</figref> where the width <b>250</b> and the height <b>255</b> of each document <b>200</b> are magnified while the margins <b>220</b>, <b>225</b> are kept constant, or fixed, and therefore not magnified. In contrast, as illustrated in <figref idref="DRAWINGS">FIG. 14</figref>, an embodiment of the present invention assembles the margins <b>220</b>, <b>225</b> with their respective width <b>250</b> and the height <b>255</b> of the document <b>200</b> prior to magnification. It has to be noted that the horizontal margin <b>225</b> between two adjacent documents <b>200</b> is divided in two (2) and equally shared on both sides to form the margins on the adjacent sides of the two (2) adjacent documents <b>200</b>. This way, both the document <b>200</b> and its surrounding margins <b>220</b>, <b>225</b> are magnified together. The magnification and/or reduction therefore considers each document <b>200</b> and its surrounding margins <b>220</b>, <b>225</b> as being a single object <b>260</b> as illustrated in <figref idref="DRAWINGS">FIG. 15</figref>. All the juxtaposed objects <b>260</b> on a plurality of axes of documents can be magnified/reduced without creating a difference as previously explained in respect with <figref idref="DRAWINGS">FIG. 11</figref> and <figref idref="DRAWINGS">FIG. 12</figref>.

0116<figref idref="DRAWINGS">FIG. 16</figref> illustrates two juxtaposed axes of documents <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b> having a plurality of objects thereon. All the margins (visible in <figref idref="DRAWINGS">FIG. 13</figref> with reference numbers <b>220</b>, <b>225</b>) are comprised in each object <b>260</b> with their respective document <b>200</b> (visible in <figref idref="DRAWINGS">FIG. 13</figref>). A magnification of the collection of objects <b>260</b> from <figref idref="DRAWINGS">FIG. 16</figref> by a factor of two (2) gives the rendering of <figref idref="DRAWINGS">FIG. 17</figref> where no discrepancies in object <b>260</b> resective positions have been created. Again, a magnification of the collection of objects <b>260</b> from <figref idref="DRAWINGS">FIG. 16</figref> by a factor of four (4) gives the rendering of <figref idref="DRAWINGS">FIG. 18</figref> where no differences in object <b>260</b> positions have occurred.

0117Once the magnification of the objects <b>260</b> has been made, the margins <b>220</b>, <b>225</b> are extracted from the magnified object <b>260</b> as it is explained below. The general equation exemplified in Equation 2 stipulates that c is the total document size, m₁is the size of one of the two margins and m₂is the size of the other margin. Therefore, the size, in one direction, of an object is defined by Equation 2 that can also take into consideration intentional variation in margins sizes.

0000<br /><i>f</i>(<i>c</i>)=<i>c−m</i>₁<i>−m</i>₂  Equation 2

0118The illustrative object <b>260</b> used in the present embodiment illustrated in <figref idref="DRAWINGS">FIG. 19</figref> has a square or a rectangular shape. The general equation exemplified in Equation 2 can be adapted to calculate the size of the space within the margins in a magnified and/or reduced document—or any graphical object—<b>260</b>, by a factor α, in the x direction and in the y direction, as exemplified in Equation 3. The space within the margin, delimited by arrows s_xand s_yin <figref idref="DRAWINGS">FIG. 19</figref>, is going to be referred as an internal space. The total document size, delimited by arrows c_xand c_y, is going to be referred as an object container.

0000<br /><i>s</i>_x<i>=f</i>(<i>αc</i>_x)=α<i>c</i>_x<i>−m</i>_x1<i>−m</i>_x2

0000<br /><i>s</i>_y<i>=f</i>(α<i>c</i>_y)=α<i>c</i>_y<i>−m</i>_y1<i>−m</i>_y2  Equation 3

0119<figref idref="DRAWINGS">FIG. 19</figref> shows a document that has a different aspect ratio than the object container <b>260</b> discussed above. Let us consider the magnified and/or reduced document dimension o′_xand o′_ywe are trying to calculate. For maximum use of the internal space, the object <b>200</b> is magnified vertically. The same magnification ratio is used horizontally to keep the image aspect ratio. The next equations could be reversed to accommodate a portrait-oriented document. The calculation of the final width of the magnified/reduced document is then calculated by keeping the ratio from the original dimension of the document o_xand o_y.

0000<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mfrac><msubsup><mi>o</mi><mi>x</mi><mi>′</mi></msubsup><msubsup><mi>o</mi><mi>y</mi><mi>′</mi></msubsup></mfrac><mo>=</mo><mfrac><msub><mi>o</mi><mi>x</mi></msub><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><msubsup><mi>o</mi><mi>x</mi><mi>′</mi></msubsup><mo>=</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><msubsup><mi>o</mi><mi>y</mi><mi>′</mi></msubsup></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow></mrow></mtd><mtd><mrow><mi>Equation</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>4</mn></mrow></mtd></mtr></mtable></math></maths>

0120In Equation 5, A “padding” area, p_x1and p_x2, is used to accommodate document <b>200</b> shape variations without effecting a “general” transformation process into an object <b>260</b>. The formulas used to consider the padding area are expressed in Equation 4 that follows.

0000<br /><i>s</i>_y<i>=o′</i>_y<i>=αc</i>_y<i>−m</i>_y1<i>−m</i>_y2

0000<br /><i>s</i>_x<i>=o′</i>_x<i>+p</i>_x1<i>+p</i>_x2<i>=αc</i>_x<i>−m</i>_x1<i>−m</i>_x2

0000<br /><i>p</i>_x1<i>+p</i>_x2<i>=αc</i>_x<i>−m</i>_x1<i>−m</i>_x2<i>−o′</i>_x  Equation 4

0121We are trying to extract the new size of the padding p_x1and p_x2. We first need to eliminate o′_xby using the result of Equation 3, we get:

0000<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mtable><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><mrow><mrow><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>=</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><msubsup><mi>o</mi><mi>y</mi><mi>′</mi></msubsup></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><mrow><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>=</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>Equation</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>5</mn></mrow></mtd></mtr></mtable></math></maths>

0122In the preferred embodiment of this invention, we center the document in the object space. To do that, we define the two padding as equals in Equation 6.

0000<maths id="MATH-US-00003" num="00003"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mi>p</mi><mi>x</mi></msub><mo>=</mo><mrow><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><mrow><mn>2</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>p</mi><mi>x</mi></msub></mrow><mo>=</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><msub><mi>p</mi><mi>x</mi></msub><mo>=</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>Equation</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>6</mn></mrow></mtd></mtr></mtable></math></maths>

0123An alternate embodiment is that the left padding has a share β and the right padding has share 1−β, where 0≦β≦1. This gives the result shown in Equation 7. This will keep proportions between left and right padding during magnification.

0000<maths id="MATH-US-00004" num="00004"><math overflow="scroll"><mtable><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><mrow><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mi>β</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><msub><mi>p</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>=</mo><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>β</mi></mrow><mo>)</mo></mrow><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>x</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>y</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>Equation</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>7</mn></mrow></mtd></mtr></mtable></math></maths>

0124<figref idref="DRAWINGS">FIG. 19</figref> and Equations 4-7 show how to calculate the width and height of a document that is maximized vertically in its space. This depends on image aspect ratio and the space available for content in the container ratio so these formulas can easily be changed to fit horizontally a document image. As a consequence of having arbitrary size of borders in the object container, one should be aware that after magnification or reduction, the available space within the container image aspect ratio may not be the same and the document image may prefer to fits on the opposite axis to maximise its display surface.

0125Equations 4-7 could be easily reproduced in order to maximize an object horizontally, as seen in Equation 8.

0000<maths id="MATH-US-00005" num="00005"><math overflow="scroll"><mtable><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><mrow><msubsup><mi>o</mi><mi>y</mi><mi>′</mi></msubsup><mo>=</mo><mfrac><mrow><msub><mi>o</mi><mi>y</mi></msub><mo></mo><msubsup><mi>o</mi><mi>x</mi><mi>′</mi></msubsup></mrow><msub><mi>o</mi><mi>x</mi></msub></mfrac></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><msub><mi>s</mi><mi>x</mi></msub><mo>=</mo><mrow><msubsup><mi>o</mi><mi>x</mi><mi>′</mi></msubsup><mo>=</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><msub><mi>p</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mi>β</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>y</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>x</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><msub><mi>p</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>=</mo><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>β</mi></mrow><mo>)</mo></mrow><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mi>o</mi><mi>y</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>α</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>c</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow><msub><mi>o</mi><mi>x</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>Equation</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>8</mn></mrow></mtd></mtr></mtable></math></maths>

0126<figref idref="DRAWINGS">FIG. 20</figref> illustrates two axes of objects <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b> with appended header <b>265</b>. <figref idref="DRAWINGS">FIG. 21</figref> illustrates objects that are a magnification of objects from <figref idref="DRAWINGS">FIG. 20</figref> by a factor of two (2) and <figref idref="DRAWINGS">FIG. 22</figref> illustrates objects that are a magnification of objects from <figref idref="DRAWINGS">FIG. 20</figref> by a factor of four (4). It can be appreciated that there is no longitudinal relative discrepancy between axis of objects <b>210</b>.<b>1</b> and axis of objects <b>210</b>.<b>2</b> despite the magnification. However, in the present embodiment illustrated in <figref idref="DRAWINGS">FIGS. 20-22</figref>, the header <b>265</b>, intervening space <b>270</b> between the header <b>265</b> and its adjacent axis of objects <b>210</b>.<b>1</b> and inter-axis space <b>275</b> have respective fixed thicknesses.

0127Moving now to <figref idref="DRAWINGS">FIG. 23</figref> through <figref idref="DRAWINGS">FIG. 25</figref> illustrating an alternate embodiment to the embodiment illustrated in <figref idref="DRAWINGS">FIG. 20</figref> through <figref idref="DRAWINGS">FIG. 22</figref>. In the embodiment of <figref idref="DRAWINGS">FIG. 25</figref> through <figref idref="DRAWINGS">FIG. 25</figref>, the intervening space <b>270</b> between the header <b>265</b> and its adjacent axis of objects <b>210</b>.<b>1</b> and the inter-axis space <b>275</b> are absent to maximize the useful display area and also to simplify the rendering of the axes of objects <b>210</b>.

0128The linear expansion <b>280</b> an axis of objects <b>210</b>.<b>1</b>, <b>210</b>.<b>2</b> or a group of axes of objects as shown in <figref idref="DRAWINGS">FIG. 26</figref> is a resultant of the magnification process. The visual rendering of the linear expansion of the axes of objects <b>210</b> can be directed by applying expansion anchors <b>290</b> to the group of axes of objects <b>210</b>. The expansion anchors <b>290</b> of the present embodiment draw a vertical axis <b>295</b> at which the expansion of the axes of objects <b>210</b> remains fix and from which they can expands from both sides <b>300</b>, <b>305</b>. In the present situation the expansion anchors <b>290</b> are disposed on the extreme left side of the axes of objects <b>210</b> and expansion <b>280</b> only happens toward the right side <b>300</b>. The effect of expansion toward the right <b>300</b> where the axes of objects <b>210</b> remain fixed along the vertical axis <b>295</b> defined between the two expansion anchors <b>290</b> can be appreciated from <figref idref="DRAWINGS">FIG. 26</figref> and <figref idref="DRAWINGS">FIG. 27</figref> illustrating a magnification by a factor of two (2) and <figref idref="DRAWINGS">FIG. 28</figref> that illustrates a magnification of objects in <figref idref="DRAWINGS">FIG. 26</figref> by a factor of four (4).

0129Still on <figref idref="DRAWINGS">FIG. 26</figref> through <figref idref="DRAWINGS">FIG. 28</figref> one can appreciate that a document border <b>310</b>, or an object border in the present example, can either remain with a fixed width <b>315</b> or be magnified with the object <b>320</b>. The fixed width object border can be considered as a part of the margin in the object container illustrated in <figref idref="DRAWINGS">FIG. 19</figref>.

0130<figref idref="DRAWINGS">FIG. 29</figref> shows that the expansion anchors <b>290</b> and its related vertical axis <b>295</b> can be horizontally movable to locate the vertical axis <b>295</b> at the desired position. The vertical expansion anchors <b>290</b> (now <b>290</b>.<b>1</b>) and its related vertical axis <b>295</b> (now <b>295</b>.<b>1</b>) are paired with a complementary horizontal expansion anchors <b>290</b>.<b>2</b> and a related horizontal axis <b>295</b>.<b>2</b> that can be vertically moved to locate the horizontal axis <b>295</b>.<b>2</b> at a desired location. The intersection of the vertical axis <b>290</b>.<b>1</b> and the horizontal axis <b>290</b>.<b>2</b> creates an expansion point <b>310</b> bout which expansion/reduction in all directions will occur.

0131The vertical expansion anchors <b>290</b>.<b>1</b> of the embodiment depicted in <figref idref="DRAWINGS">FIG. 30</figref> can be used without the vertical axis <b>295</b>.<b>2</b> (not shown on <figref idref="DRAWINGS">FIG. 30</figref>). Similarly, the horizontal expansion anchors <b>290</b>.<b>2</b> can be used without the horizontal axis <b>295</b>.<b>2</b> (also not shown on <figref idref="DRAWINGS">FIG. 30</figref>). The vertical expansion anchors <b>290</b>.<b>1</b> can discretely be positioned between two objects <b>260</b>.<b>3</b> and <b>260</b>.<b>4</b> on axis of objects <b>210</b>.<b>1</b> (could be made in respect of any other axis). Likewise, the horizontal expansion anchors <b>290</b>.<b>2</b> can discretely be positioned between two axes of objects <b>210</b>.<b>1</b> and <b>210</b>.<b>2</b>.

0132The expansion anchors <b>290</b> can alternatively be disposed adjacent to their respective edges <b>225</b>, <b>230</b> of a display <b>320</b>. This precise location for the expansion anchors <b>290</b> is convenient and intuitive for a user. A user could understand that the expansion anchor can be slided along the edge <b>225</b>, <b>230</b> of the display <b>320</b> while not taking much space toward the center of the display <b>320</b>. The vertical axis <b>290</b>.<b>1</b>, the horizontal axis <b>290</b>.<b>2</b> and the expansion point <b>310</b>. Can selectively be displayed only when the expansion anchors are moved and disappear from the display <b>320</b> after a period of time.

0133Additional embodiments for determining the expansion point <b>320</b> are illustrated in <figref idref="DRAWINGS">FIG. 31</figref>. Firstly, an object <b>260</b>, <b>335</b> can be selected to serve as the expansion point from which the expansion will occur. The selected object <b>335</b> is illustrated as being selected with a distinctive frame <b>340</b>. Secondly, the position of a pointer <b>345</b> can alternatively be used to serve as the expansion point from which the expansion will occur.

0134<figref idref="DRAWINGS">FIG. 32</figref> through <figref idref="DRAWINGS">FIG. 35</figref> illustrate that the magnification and/or the reduction can be non-isometric (anisometric). That is to say that the magnification can be made only horizontally as depicted in <figref idref="DRAWINGS">FIG. 33</figref> or be made only vertically as depicted in <figref idref="DRAWINGS">FIG. 34</figref>. The border <b>310</b> can remain of a fixed width <b>315</b> as illustrated in <figref idref="DRAWINGS">FIG. 32</figref> through <figref idref="DRAWINGS">FIG. 35</figref> to remain consistent with the portion of the object <b>260</b> that remains unmagnified. Consider α_xand α_yas magnification factor horizontally and vertically. Equation 9 shows how to calculate the internal space s_xand s_y, the object dimension o_xand o_y, and the padding p_x1and p_x2adapted from Equation 3 through 8. Note that like in Equations 4-8, the document image aspect ratio and the available space within the container image aspect ratio should be considered to determine if the image should be maximized horizontally or vertically.

0000<maths id="MATH-US-00006" num="00006"><math overflow="scroll"><mtable><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><mrow><msub><mi>s</mi><mi>x</mi></msub><mo>=</mo><mrow><mrow><msub><mi>α</mi><mi>x</mi></msub><mo></mo><msub><mi>t</mi><mi>x</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>m</mi><mrow><mi>x</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><msub><mi>s</mi><mi>y</mi></msub><mo>=</mo><mrow><mrow><msub><mi>α</mi><mi>y</mi></msub><mo></mo><msub><mi>t</mi><mi>y</mi></msub></mrow><mo>-</mo><msub><mi>m</mi><mrow><mi>y</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" 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0135<figref idref="DRAWINGS">FIG. 36</figref> depicts various different shapes of objects <b>200</b> using in a variety of ways the padding area p within the margins <b>220</b>, <b>225</b>.

0136<figref idref="DRAWINGS">FIG. 37</figref> shows the same shapes of <figref idref="DRAWINGS">FIG. 36</figref> magnified. One can appreciate the way margins remains fixed while the shape of object grows to the maximum size within these margins.

0137As in <figref idref="DRAWINGS">FIGS. 36-37</figref>, the object container and the margin may also use a variety of shapes. The particular formulas are not described here since all shape should be defined differently. Formulas referred above can be adapted by defining a padding margin around the subject shape.

0138Moving now to <figref idref="DRAWINGS">FIG. 38</figref> illustrating another embodiment. Two groups of axes of documents <b>210</b> are shown. In this case, all documents <b>260</b> of each axis <b>210</b> have equal sizes. <figref idref="DRAWINGS">FIG. 39</figref> shows the same two groups, now with the axis of document <b>210</b>.<b>1</b>.<b>2</b> reduced. This kind of magnification or reduction may not keep alignment between documents. Somehow, on a display, the position of the view may be kept centered on the magnified or reduced axis of document so the user does not lost its focus on the axis that is being magnified or reduced.

0139Non-parallel axes of documents may be used in a way described in the United States patent application publication referred to at the beginning of the present patent specification that is incorporated herein by reference. On <figref idref="DRAWINGS">FIG. 40</figref>, the space between the two groups <b>220</b> and the height of the headers <b>265</b> may be fixed or subject to resizing after magnification or reduction. A readjustment may be made on the space between the two groups <b>220</b> in other to prevent post magnification misalignment like shown after a magnification of a factor of two in <figref idref="DRAWINGS">FIG. 41</figref>. This readjustment may be made to keep the original positional aspect on documents <b>260</b>.<b>1</b>, <b>260</b>.<b>2</b> and <b>260</b>.<b>3</b>.

0140Another application of the method described in this patent application publication concerns document display systems like word processors, document viewer like a PDF viewer and webpage browsers. <figref idref="DRAWINGS">FIG. 42</figref> depicts a layout used in a webpage <b>300</b>. There may be a page margin of size p_xand p_ythat encapsulate the webpage content <b>310</b>. The webpage may content different part of text <b>320</b> and objects <b>350</b> such as images, chart, applet, internal frame, etc. that are presented. The webpage browser may keep margins p_xand p_yfixed and maximize space for the content <b>310</b>. After magnification shown in <figref idref="DRAWINGS">FIG. 43</figref>, the size of the text <b>320</b> may be scaled at the same factor than the magnification of webpage content <b>310</b>. This ratio may also be applied to the space reserved to the object <b>350</b>. Consider q_xand q_y, the right and bottom margin of the object <b>350</b>. These margins can also be considered as fixed and the object <b>350</b> could be maximized in the space reserved within the margins by applying the formula described in Equation 3 recursively. One can appreciate in <figref idref="DRAWINGS">FIGS. 42 and 43</figref> the way the right side of the object <b>350</b> is aligned with the text <b>325</b> and <b>326</b> after magnification. This shows how the object size is magnified to save more space after magnification and gives more to the content that is being shown.

0141The description and the drawings that are presented above are meant to be illustrative of the present invention. They are not meant to be limiting of the scope of the present invention. Modifications to the embodiments described may be made without departing from the present invention, the scope of which is defined by the following claims: