Cartesio is a freeware computer program, dedicated to the spatial study and understanding of planar projective configurations, including orthographic projections, axonometry (orthographic and oblique) and perspectives.
Furthermore, operating analytically, it is also useful as a first approach to the CAD and computer graphics.
The use of the software consists of opening one to six projection windows, loading one or some solids and modifying the characteristics of the projections using the keyboard or mouse.
There are three possible methods to begin a work session:

After opening a window of projection, pressing CTRL+F1 a menu option with information appears, which is relative to the projection contained in the active window.
It is also possible to transform an any size DXF file as long as it contain 3D face, lines and other 2D or 3D entities.

The freeware Cartesio
Studying projective geometry, one often becomes absorbed trying to understand the spatial configuration of a projection and its results on the projection plane.
How is the object placed with respect to the axis, and the projection plane in respect to the object and to the center of projection?
Does the direction of projection affect the picture perpendicularly or is it inclined and by how much?
Very often the answers given are imprecise or even wrong, given the difficulty in finding secure and not just deductive evidence and the difficulty in always foreseeing the position of the elements in the three dimensions of space and their projection on one plane.
CARTESIO, the software illustrated in this short manual, helps find the answers to these and other possible questions in the field of projective geometry, both visually and numerically.
It does not limited itself to supplying the orthographic, axonometric or perspective projection of one or more objects – like a calculator that supplies the result of a complex operation and like a CAD software – but above all it allows the analysis and evaluation of all the surrounding elements which are essential to a complete understanding of the mechanism of projection.
Very often the student reduces the spatial complexity of the projection to a series of simpler and more and mechanical bi-dimensional operations, to a procedure which does not, however, include a faint "memory" of the original reasons.
The student is perhaps able to produce a correct graphic but without a clear understanding of why it should be laid out in that way, almost as if he is following a more or less precious and well kept recipe.
Apart from leading to huge mistakes, this habit reduces spatial understanding and the same capacity to interpret a picture.
With the invention of CAD the simple manual practice of a drawing is less and less necessary, giving rise to the risk of removing the last slim umbilical cord that links the project to its representation, a phase which helps the projector to "know" the objects he is creating.
Seeing, understanding and drawing are therefore three important rings in the planning, especially in architecture and are cardinal in the field of representation. Along side the necessary theory but without trying to replace it, Cartesio allows these essential aspects to be studied in detail thus supplying a complete taxonomy of projective methods.
Apart from the predefined projections, the user will be able to construct a generic projection for each class, directly emitting the data of construction.
For all the projections it is able to modify the forms of representation, for example by turning the direction of projection around the axis origin; maintaining, however, the relationship between the view window and the class of projection.
In this way it will be possible to test all the possible configurations of a class, comparing the visual results with a series of numerical information.
For example the angles between the plane of projection and the axis or the Cartesian planes or the angles formed between them by the projected axis or the foreshortening of versors placed along the axis.
For each projection the user will always see (in four different forms: three orthographic and one axonometric projection) the arrangement of the projection plane and the direction of projection in respect to the axis and if desired, the line of the horizon and the circle of the distances in the perspective projection or also, in one or more projections, the projection plane relative to another projection of reference.
How can the representation be modified and how do the relative numerical values change, moving, for example, the center of projection a little towards the right or left in a frontal perspective projection?
Or by moving the center of projection of the object closer or further away?
Very often the careful analysis of the results and parameters allows the student to understand the projective mechanisms better and to create that store of knowledge and experience which is necessary to both the production of drawings and their correct understanding.
Apart from its complete control of projective parameters, CARTESIO is also introductory to the use of CAD software, not only permitting all the possible geometrical transformations, the sections of the solids or their deformation but above all, allowing the analysis and the use of the transformation matrixes (geometrical and projective), logical base of the graphic software electronic elaboration.
The student will therefore become familiar with concepts and methods which he will later come across in a more cryptic and often implicit form in software of computer graphics and in CAD.
For example, it will be possible to construct an axonometry of a perspective or vice versa, or to verify the effects of a matrix of geometrical transformation applied to selected points.
The results, for example, of the rotation of an object around a generic axis will have an immediate visual and numerical impact on the student and he will be guided towards the use of the purely numerical-mathematical software, a typical characteristic of the CAD software.
Designing with CAD software requires a complete methodological revision. For example, whereas traditional drawing generates the representation of the projected model (a model that remains eminently "mental"), in designing aided by a computer the model itself is constructed in three dimensions almost as if it were a concrete model.
From this the representations which are desired and necessary both to an understanding and to a visual transmission and to its construction can be drawn.
The knowledge of the bases of analytical geometry is not only a solid basis for those who are ready to use the CAD, united with the descriptive geometrical principles, but it also allows one to "see" and organize the space, to investigate in detail and to find analytical comparisons to graphical methods or vice versa.
In short, for those who really want, to understand.

The choice of a command
Normally the first operation to be carried out, after the software Cartesio has been started, is to open a window using the menu option Projections.
It will then be necessary to choose one or more solids from the menu Solids.
At this point all other menus will be activated.
However, to modify the projective configuration it is necessary to use the keyboard.
It is sufficient to press CTRL+F1 to obtain information regarding which keys to use to modify the active projection.

Keys used to modify the projections
In Windows operative system, the mouse is an almost irreplaceable instrument. It therefore plays an important role in Cartesio, as in any other software of that system.
For example, the operations of zoom, pan and visualization of the coordinates can be activated just using the mouse. The selection of the commands from the menu can also be carried out using the keyboard but is much easier using the mouse.
Nevertheless, once the representation or representations and the solids to be represented have been selected, the modification of the characteristics of the representation itself is mainly done using the keyboard
Each type of projection only "sees" certain keys: the following will now illustrate the keys used for each projection for the modification of the characteristics of each type of projection.
For example, for the orthographic projections only the arrow keys are used while for the perspective projections many other keys are used.
If keys are pressed that are not valid for the projection active at that moment a sound will be emitted to indicate it is impossible to carry out the command.
Using the sequence CTRL+F1 in Cartesio a menu is activated which shows the keys necessary for the modification of the active projection.
In general the following categories of keys are used:
Arrow keys or also the keys 8, 2, 6, 4.
These keys are marked with an arrow going upwards, downwards, to the right and to the right. They are generally placed on the right hand side of the keyboard.
Numeric keys can also be used – both those of the numeric key board or the numbers at the top of the keyboard.
They key corresponding to number 8 is the upwards arrow, number 2 is the downwards arrow, number 6 is the arrow to the right and number 4 is the arrow to the left.

RETURN
Is generally found on the right hand side of the keyboard.
It is useful for the menu options and is equivalent to the key OK of the same menu.

ESC
Is normally found in the upper left hand corner. It is equivalent to the key CANCEL of the same menu.

F1
The "function" keys are found in the upper part of the keyboard, at the same height as the key ESC.
In general there are twelve function keys (from F1 to F12), divided in three groups of four keys.
In Windows F1 is usually the equivalent to asking for help (help on line).
In Cartesio it is used, together with the key CTRL to obtain a menu of help for the projection which is active at that moment.
It is ignored if there are no active projections.
If you only press F1 a menu appears of general help; it is valid for all projections and relative to the use of the mouse and other generic keys.

Alpha-numerical keys
These keys correspond to a letter of the alphabet and numbers from 0 to 9.
In Cartesio only some of these keys are used:
U, D, L, R, X, Y, Z, + (plus) and – (minus) and the numbers excluding 0 and 5.
The meaning of the keys can change from projection to projection: for example, the keys X, Y and Z, define the receding axis in oblique axonometric projection, whereas in perspective they move the view point and the main point together along the axis X, Y or X.
In perspective, instead, U move up, D move down, L move left and R move right the viewpoint respect the projection plane origin.
In predefined di-metric and tri-metric orthographic axonometry X, Y and Z define the preferential axis of shortening. In the menu options the numeric keys, including the full stop (.) and the sign – (minus) are often used for the emission of co-ordinates and other values.
PgUP and PgDn or also the keys 9 and 3 are found above they arrow keys and correspond to the keys 9 (PgUP) and 3 (PgDN) of the small numerical keyboard if present.
For the oblique di-metrical projection they are used to modify the coefficient of foreshortening along the receding axis (increasing it with PgUP and decreasing it with PgDN).
In the other cases it increases or decreases, both angularly and linearly.

HOME and END or also the keys 7 and 1
These keys are also placed above the arrow keys (to the left of PgUP and PgDN) and in correspondence to the keys 7 (HOME) and 1 (END) of the numeric key board.
They are only used in the perspectives (all types) to bring closer (HOME) or to go further away from (END) the viewpoint from the principal point.

"Alternative" keys
These are the keys SHIFT, CTRL, ALT and ALT GR (not always present).
They are usually used together with other keys.
First the alternative key must be pressed and then, while keeping the former pressed, the other key (for example a letter of the alphabet, a number or an arrow) or also the left button on the mouse.

SHIFT
Is generally placed below the key RETURN.
It is found both on the right and on the left of the keyboard.
It is used to capitalize letters: SHIFT + a means the letter A.
In Cartesio it is usually ignored since both capital and small letters are accepted.
The only exception is its use in combination with the left button of the mouse.
In this case the distance between two points on the plane of projection is calculated.

ALT
Is normally found on the left side of the space bar (which is at the bottom of the keyboard), in Windows it is used to selection the options of the menu (by pressing ALT+underlined letter of the menu to be activated).
It is only used in Cartesio to select an option of the menu.

CTRL
Generally placed at the bottom both on the right and left of the keyboard. In Cartesio it is only used together with the arrow keys right and left for the oblique plane perspectives and the generic oblique axonometric projections and with the four arrow keys for the generic oblique axonometric projection and the generic orthographic axonometry as well as in combination with the keys X, Y and Z for all projection plane perspectives to move the line PV-PP.
It is also used together with the function F1 to obtain help relative to the active window and together with the left button of the mouse (only for orthographic projections) to visualize the co-ordinates of the point indicated by the crossed cursor.

ALT GR
If present, it is found to the right of the space bar; in Cartesio it is equivalent in every aspect to the key CTRL.

Use of the mouse for projections
Left button of mouse: ZOOM function.
If pressed only once the top of the window of enlargement can be located.
By keeping it pressed down the size of the window of zoom can be defined.
By releasing it the part of the drawing seen in the window is enlarged.

Right button of mouse: PAN function.
The PAN function allows you to move the window of view without changing the size.
If pressed once the starting point of movement can be located.
By keeping it pressed the size and direction of movement can be defined.
By releasing it the window in view is moved in regard to the objects which are represented.

SHIFT + left button of mouse: function of calculation of distance between two points on the projection plane.
This function allows the calculation of the distance between any two points on the plane of representation and projection.
In an anti-clockwise direction the angle between the horizontal line and the line that unites the initial point and the one actually indicated by the mouse cursor is also calculated.

In Windows 9x and NT the pressure on the left button of the mouse activates the window where the graphic cursor is placed. Therefore, if the command "zoom" or "distance calculation" is carried out on an inactive window, this will automatically become active and the zoom and calculation of distance will be carried out.
Vice versa if the pan function is carried out (right button of mouse), it is possible to identify the two points also outside an active window.

Starting Cartesio
To start Cartesio a double click with the mouse on the software icon is sufficient. A menu will appear on the desktop of Windows which gives some information about the software and how to look for help on line.
To enter into the actual program move the cursor to the key OK and click one or press the key RETURN or also the space bar.
The initial configuration of Cartesio corresponds to a typical Windows software.
At the beginning only three of the various options of the menu are activated: File, Projections and Help (in Italian language).
In fact, at the beginning of a work session it is possible to only open one new window of projection (using the menu Projections) or by calling a configuration of projections, which was previously memorized, using the combination File-Open.
The use of the software consists in recalling on the screen of one or more windows (up to a maximum of six), each containing data projection, either orthographic, orthographic axonometry, oblique axonometry or perspective; load then one or more pre-defined solids (up to a maximum of six) or a file DXF produced by AutoCAD or other software and modify the characteristics of the projections to verify their configurations or apply to the solids geometric transformation, section or solid deformation.

Opening a window of representation
A window is now activated containing an orthographic projection by moving the mouse to the menu voice Projections, and clicking the left button, still pressing the key and moving the mouse to highlight the voice Orthographic projections before releasing it.
It is also possible to open a new window using only the keyboard, activating the menu Projections with the combination of the keys ALT+P (the underlined letter of the voice Projections) and choosing the orthographic projection by clicking the underlined letter: in this case the letter O (either capital or small).
The various projections available are divided into homogeneous groups: orthographic projections, orthographic axonometry, oblique axonometry and perspective.
Each window of representation could modify the projective modality but always remains within its class.
In this way, for example, the orthographic projection window could represent one or more objects in any of six possible orthographic projections (top or bottom view or all four front views), while a parallel plane perspective window will always keep the picture plane parallel to two Cartesian axis while still being able to modify the position of the center of projection and the distance from this projection plane.
This characteristic is particularly useful when operating more than one window of representation especially when modifying the initial parameters by default: at each moment it is certain that what is written at the top of the window of representation corresponds to the effective projection it contains.

Analysis of a window of representation
A window of projection, no matter what type of projection, is always divided in three areas:
A central graphic zone in which the selected objects will be represented.
This area usually contains a reference grid, the position of which can be selected using the combination Windows-Grid step and plane…, but only after having chosen a solid from the menu Solids.
In this area the mouse cursor takes on the configuration cross hair, typical of CAD software and useful for the clear identification of a point in the graphic area.
A control area (which can be deactivated) on the right-hand side, which includes some graphics the meaning of which will be analyzed later on.
A line of text at the bottom which contains alphanumerical indications relative to the projection.
Furthermore, for each projection there is a corresponding menu option (which can be activated with the combination File-Informations) which contains all the numerical information relative to the projection.
To enlarge the window, click the button in the upper right hand corner of the window itself.
As in any window of Windows, this button allows the maximum enlargement of the window.
On the other hand, the button next to it allows you to reduce the window to an icon; to make it visible again a double click on the same icon is sufficient.
The meaning of the graphics placed on the right of the window is as follows:
At the bottom the axis X, Y and Z are represented as they are placed on the plane of projection.
The length of the axis in this graphic is not defined but the relative lengths are proportional: thus, if a unitary versor along the X axis is projected in the picture with a length equivalent to half of the same versor along the Y axis, in the graphic the two axis will be represented so that one (axis Y) is double the other (axis X).
To facilitate the immediate recognition of the axis they are shown in different colors: axis X is blue, axis Y is red and axis Z is yellow.
On the other hand, the tern of axis represented in the center of the window graphic is according to scale with the objects and the grid and therefore the length of the axis may vary according to the scale of representation.
To modify the length of these reference axis (initial length 0.5 units), it is necessary to use the sequence File-Preference-Axis scale into projections…
The axis X, Y and Z, the projection plane (in blue) and the direction of projection (in green) are represented at the top in orthographic isometric axonometry from the first positive square.
This allows the spatial comprehension of the projective configuration present at that moment in the graphic area of the window.
The three lower graphics represent the same elements (axis, projection plane and direction) respectively seen from a top view, in front elevation view negative from Y and lateral elevation view positive from X.
The combination of these four graphics together with the indications of the graphic at the bottom supply extremely detailed information regarding the disposition of the picture and of the direction of projection in relation to the Cartesian axis.
The fifth graphic identifies the portion of the image which is represented at that moment in the window: the dark part shows the rectangle which contains the image while the empty rectangle identifies the internal part of the window.
The line of text at the bottom contains some simple information relative to the projection.
Furthermore, by using the command File-Make information file…, it is also possible to create a file (with a suffix at the end INF) which contains all indications in the image, information and also, for each open window, the matrix of projective transformation, the equation of the plane of projection and the coordinates of the three or four points which characterize the plane of projection.

Choosing one of the predefined solids
After having opened the first window of representation and having enlarged the screen completely, one of the predefined solids must be selected from the menu Solids.
Move the mouse to the item Solids and keeping the left button pressed down, lower the cursor to the voice Vacuous platonics, then moving it to the item Vacuous tetrahedron on the sub-menu.
In this way an item is selected operating the menu at more than one level: this modality, which is characteristic of Windows, will be used on many more occasions.
A hollow solid-edged tetrahedron will now appear on the screen, that is to say, consisting of angles in the form of crossbars in red.
It is possible to load up to six solids in the picture as long as the total of their faces is less than or equal to 1000.
Each solid will be a different color: the first red, the second yellow, the third green, the fourth light blue, the fifth dark blue and the sixth solid magenta.
An explanation of how to erase or change color of the solids will be explained but they will always be selected according to their color.
The following predefined solids are available: the five platonic solids or regular polyhedra (tetrahedron, cube, octahedron, icosahedron, dodecahedron) and a corresponding number of other hollow solid-edged Platonic solids (star polyhedra and truncated polyhedra, with reference to the Archimedean solids or semi regular polyhedra).
Furthermore, the following also appear: a sphere formed with seventy-two faces, a mazzocchio with twelve octagonal sectioned parts, a vacuous mazzocchio consisting of seven hexagonal sectioned parts and a simple construction of example.
Finally, there are three families of regular solids: prisms, pyramids and truncated pyramids.
Each of these solids could have between three and thirty sides, thus defining also cylinders, cones and truncated cones.
Each solid can be deformed to obtain, for example, an ellipsoid from a sphere or an elliptical based cylinder or a rectangular or trapezoidal-based pyramid.
In the menu File the command Make coordinate file… comes up and generates a CDR type of file, containing the real coordinates of the points that form the model present at that moment in Cartesio (including the indications regarding color and face number) and, for each window of projection, the coordinates of the points of the faces projectively transformed, some basic indications for the identification of the projective parameters and the matrix of projective transformation.

Modifying the representation
Each window of representation corresponds to a type of projection but each type can be configured in various sub-types: for example in the case of orthographic projections there are six possible configurations.
The software opens a window of representation with a sub-type of projection by default, modifiable using the keyboard.
The modification of the representation only occurs if at least one solid has been loaded in the current drawing.
In the case of orthographic projection using the four arrows on the key board, it is possible to run through all six configurations: by pressing the downwards arrow the planar representation with a bottom view appears whereas the arrow pointing to the right runs through the four representations in front view in an anti-clockwise direction (the left arrow runs through them in the opposite direction).
The orthographic projections include another interesting possibility: that of being able to identify the coordinates of any point on the screen.
For obvious reasons of clarity this option is only valid for orthographic projections, but apart from the plan also for the elevated ones: it is obvious in this case that the coordinates that can be "read" on the screen are X (or Y) and Z.
To activate the view of the coordinates, first press the key CTRL and then the left button of the mouse.
At that point it is possible to release the key CTRL and as long as the left button on the mouse is pressed down, the co-ordinates relative to the position of the graphic cursor will be represented, in the bottom right hand corner of the window of representation in the form X, Y and Z.
To activate the function that allows you to see the distance and angle of the point indicated in respect to the point occupied by the cursor at the beginning of the operation to calculate the measurements of the plane of projection, press both the key SHIFT and the left button of the mouse at the same time.
The angle is calculated in an anti-clock wise direction, starting from the X-axis of the picture.
In the case of orthographic projections or oblique axonometry for which the plane of projection is parallel to the picture, the distance is the actual one.
In all other projections the distance shows, since it is calculated on the picture, the foreshortening undergone by one segment in its projection on the plane.
To vary the number of decimal numbers of the coordinates or the values of angle and distance activate the sequence File-Preference-Coordinate decimals… and a value of decimals including and between 0 and 5 is supplied.
To obtain brief help on line, without activating the general help it is useful to remember that the keys to use for the modification of the projections are the sequence CTRL+F1.
A menu option thus appears which is specific and relative to the projection in the window active at that moment.
By simply pressing F1 a general menu can be seen which is valid for all projections.

Modification of the projection window
When loading a solid in the picture it can be noted that, when opening the projection window, the grid is denser and the axis smaller and that the section shown on plane has been modified in the moment that the solid was called to the screen.
Cartesio automatically organizes all the objects present within a small frame.
This occurs each time a new solid is called upon or every time the projection is modified, for example passing from plane to perspective and vice versa.
The user can, however, within certain limits, enlarge or make the plane area shown in the projection window smaller: only the window being viewed will be modified in its dimension or position, not the actual size of the solids being represented.
By clicking the button in the top right hand corner of the projection window it is enlarged to the whole screen; thus, by keeping the size of the projection window constant (the viewport) it is possible to modify the size of the view window (the window).
To modify the view window both buttons of the mouse are used. The button on the left carries out the zoom or enlargement of part of the view window, whereas the key on the right carries out the pan, that is the movement of the view window, without changing its dimensions.
By pressing, for example, the right button of the mouse when the cursor is placed in the bottom right hand corner of the window and while keeping it pressed and moving it towards the center, an "elastic line" is activated which indicates the direction and entity of the movement from the view window.
It should be noted that the objects, the axis and the grid are not influenced by this operation; the view window that shows the plane of representation has simply moved.
The second graphic from the bottom shows this change as soon as it happens.
The dark rectangle shows the volume of the objects while the empty frame shows the area actually being shown.
If the window is moved many times in succession it is possible that a menu will appear saying it cannot continue with the pan function: indeed, the possibility of movement are not infinite even though sufficient for any experiment you wish to carry out.
To operate the zoom of the image moving the cursor to any side of the rectangle that can be seen inside the window it is necessary to press the left button of the mouse and, keeping it pressed down, move the cursor to the opposite side of the rectangle and then release it.
In this case an "elastic rectangle" appears and indicates the part of the image to be enlarged.
In this case too, it is not possible to enlarge the picture infinitely: if the limits allowed by the software are exceeded a menu will appear.
The proportions of the picture in width and height remain constant: so if a rectangular window is selected with the small horizontal side and the longer side vertical the whole rectangle will be shown, placed on the left side of the window and then all the rest of the image that the right hand side of the window can contain.
If, on the other hand, the rectangle had a horizontal side which was three times that of the vertical one, the portion of the picture shown in the rectangle would be enlarged to make it take up all the upper part of the window whereas the lower part of the winder would still contain part of the picture.
The second item (Zoom all) of the menu View which contains the three items dedicated to the zoom allows all the active solids to be shown inside the window as usually occurs when a new window of projection is opened.
On the other hand, the voice Zoom previous shows the view of the preceding enlargement and is also used to eliminate the effects of eventual changes in position.
Furthermore, it is useful when exchanging two different views quickly.
Zoom out is used to enlarge the view window using the center of the actual window as a point of reference: each successive view includes an area that is approximately 15% larger than the preceding one.
The menu View, amongst the other items that will be explained in more detail later, also shows the item Close window (at the beginning), which allows the projection window to be closed.
The window can also be closed using the key in the top left hand corner or using the key combination CTRL+F4, as in any other window of Windows.
In both cases, if the solids have been recalled, a menu appears to avoid closing a window by mistake.
Cartesio has various types of menu options: the first informative type is associated with sound, for the systems with audio linked to the exclamation mark and only has the button OK to continue. Another type has a question mark and its corresponding sound: this is used to suggest an alternative and therefore has two buttons: the first (OK) answers the question with an affirmative; the second (Cancel) answers the question negatively.
Other menu options, all with two buttons, are used for the emission of numerical data including points or angles or in the extreme case of an irretrievable error, to communicate the premature end of a work session: a session that will be automatically saved in any case in a file with the name "Cartesio" (Cartesio.coo and Cartesio.prg).
As with any window of Windows operating system, the windows of Cartesio can be modified dimensionally using the symbol in the bottom right hand corner of the frame.
If you click the button with a double arrow (in the top right hand corner), the window is reduced in size, thus making it suitable for cascaded viewing.
If the cursor is moved to the frame of the window, to the corner in the lower right hand corner, a double arrow at 45° appears which allows the modification of the dimensions and the relationship between width and height in the same window by pressing the left button of the mouse and keeping it pressed.
If, however, you want to move the window without changing the dimensions, move the graphic cursor along the line at the top, press and do not release the left button of the mouse and move the frame of the window which will assume its new position when you release the button of the mouse.
In this way, by combining what has just been seen with the possibility of reducing a window to an icon and then place more than one on the virtual surface of the screen, it is possible to view the same objects simultaneously using more than one projection.
After the last item, the menu View also contains a list of the windows which are open and shows the windows active at that moment.
By moving the mouse cursor to the name of a window and clicking it with the left button, the highlighted window will immediately become active even if it had previously been reduced to an icon.
The reduction of a window to and icon (which occurs by using the key with the downwards arrow) is very useful when there are four or more windows open and many active solids: in fact the time need to regenerate the views may take a couple of seconds especially if the solids have been sectioned. By reducing a window to an icon the time necessary for regeneration for that "view" is completely saved.
Apart from the modality shading there is another modality of projection of the solids: these can appear on the screen either defined by their shading, with or without the bounding edges, or wire-frame, that is to say that each edge that defines the solid will be shown on the screen including those that, in theory, should not be seen because they are hidden either by the solid itself or by other solids.
It is important to point out the fundamental difference between the menu Windows and the menu View: the first refers to all the windows present on the graphic screen, the second only to the window active at that moment.
The various characteristics can be varied either by choosing whether all windows (both current and future) have to have the grid, the menu, the axis or the bounding edges or not and that the solids contained in them are visible in the modalities shading or wire-frame, or (from the menu View) by deciding that only the active window has the desired characteristics.
It should however be noted that the menu Windows is of a higher priority than the menu View.
Thus, for example, if it is indicated in the first menu that all the windows have to have the grid it is not possible to have a window without. In that case the option should be deactivated in the menu Windows (in such a way that no window has the grid) and reactivate the grid in the windows in which it is desired.
The command File-Preference-Line thickness… activates a menu option for the definition of the thickness of both the lines of the edges of the solids and of the lines inside the image to the right of the window of projection.
In such a way it is possible to adapt the thickness of the lines to any graphic resolution of the screen or to the needs given by the representation.
The accepted values range from 0 and 100 (default 15) and do not refer to the number of pixel of the thickness of the lines: the value 0 simply indicates the thickness of 1 pixel while values superior to this gradually increase the thickness of the lines in close relationship to the graphic resolution of the screen.
Now activate the command Solids-Truncated pyramid…, which opens a menu option.
In the menu it is possible to define both the number of the sides of the base of the pyramid (from 3 to 30 sides) and the height of the solid and the rays of the minor and major bases.
To modify the values of default already in writing it is sufficient to move the mouse cursor to the box with the number you wish to change and, pressing and keeping down the left button, selection the text to replace it as in a normal word processor.
If you do not have a mouse it is possible to run through the various keys or boxes using the key tabulator or TAB, usually found in the left upper half of the keyboard.
When a solid is recalled it is automatically placed inside a rectangular grid of 2 units per side, starting from the point 0,0,0.
Furthermore, each solid takes on a different color which not only livens up the image but also allows the solids themselves to be recognized more easily, especially when the same solid is active more than once.

Application of geometrical transformations
In this section we look at the transformations when applied to solids present in the drawing, modifications which will be valid for all the projection windows since all windows have a single real model as a reference point.
The commands present in the menu Transformations are of interest, not only to modify the placement of the solids and to understand, for example, how to shorten the lengths in a perspective projection, but also as a first approach to CAD.
In fact the commands of this menu often require the emission of numerical co-ordinates or angular values or also the definition of planes in space: these are all concepts and methods which are frequently used in CAD software and it is often taken for granted that they have been learnt.
The menu commands can be grouped in four categories:

The first command Make selection group… identifies some of the solids present according to their color.
Cartesio foresees the use of a maximum of six solids (for a maximum of 1000 triangular faces), to which six colors are assigned: red, yellow, green, light blue, blue and magenta.
If you want to substitute one solid with another it is therefore necessary to cancel it before the substitute is recalled in the memory.
To let the software know that one intends to cancel only that solid it is necessary to carry out the command Make selection group…
Once the selection group, which can contain between zero and six colors, has been defined, the chosen colors appear in the lower right hand corner of each window.
If you select the command Transformations-Erase solids…, specific confirmation is required.
At this point a possible new solid will take the place of the first solid that was cancelled.
Another action that explicitly requires the creation of a selection group is the change of color of one or more solids.
The command Transformations-Change solids color… activates a menu that allows the choice of color applied to all the solids in reference to the selection group.
Since all other menu commands can be annulled, they can also be recalled without an explicit selection group: if this exists the operations are applied to the selected solids; if the opposite is true they are applied to all the solids present.
There are four types of regular geometrical transformations:

Apart from this, Cartesio also foresees the multiplication of each point of the solids selected for a generic matrix of transformation, and therefore extends in a very interesting manner, above all didactically, the concept and praxis of geometrical transformation.
All the geometrical transformations can be annulled up to 100 times or carried out again so as to be able to control the effects closely.
Therefore, if there are more than 100 transformations, the first will be cancelled from the list which will only contain the last 100.

 

CARTESIO: interactive application and learning of projective geometry and computer graphics
Camillo Trevisan

Download freeware CARTESIO 3.03e, english version (592 kB)
For Windows 3.1, 95 and Macintosh (with SoftWindows software)

English translation: Christina Cawthra