Parallel Projection - Wikipedia. In your image, x and wx is the same axis, and angle is in yoz plane. Projected y: when y = 0, wy = z. cos(pi/2 - α) = z. sin(α) when y 0 and z.

Lab Exercise 5: A Camera for Simple Parallel Projection

This week we construct a module for the simplest kind of projection: orthographicparallel projection. This is the kind of projection used in engineeringdrawings, to produce 'plan views'. The projection is as follows: Givena point (x,y,z) the projection of that point is (x,y). (Alternatively,one could map to (x,z) or (y,z) depending on what kind of plan view isrequired).

Write the following code:

• A simple camera module for managing point coordinates etc
• For rendering to screen
• For performing back face elimination
• Now load 3D objects from file
• Write a program that (a) loads objects from file and then (b) projects them to screen using the simple orthographic projection camera

Your program will be assessed as part of your coursework (10%).

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Simple Camera Module

Java Programming

C Programming

Notes on Setting up the ParallelCamera

1. The drawable is the physical medium on which the image is rendered, associatedwith the camera. It plays the role of the photographic film in a real camera.
2. The boundary defined by [xmin, xmax, ymin, ymax] specifies a 2D windowon the view plane.
3. We will take the whole display area as the viewport, hence the viewportcoordinates are (0,0) to (width-1, height -1).
4. The values aX, bX, aY, bY are used to convert points on the 2D viewplaneto the 2D display. In other words, if (x,y) is a point on the viewplane,and (x',y') the corresponding point on the display, then x' = aX + bX*x,and y' = aY + bY*y. These values are defined exactly as in the notes on 2D viewing.
5. The function clickPCamera() simply computes the values of aX, bX, aY, bYgiven the values of the other parameters.

Rendering

Now we continue with the functions to actually render onto the drawableusing this camera:

Java programming

c programming

Notes

1. So the implementation of 'displayFace' is on the following lines:
• Start off a new polygon on the drawable, using 'newPolygonOnDrawable' orusing the drawPolygon method of the Graphics
  context for Java programmers;
• Suppose (x,y,z) is a vertex of the face, then its projection to the viewplane is (x,y);
• Convert this to display coordinates (x',y') = round(aX+bX*x, aY+bY*y);
• Use the 'addToPolygonOnDrawable' function to send this vertex to the drawingarea;
• When all the vertices of the polygon have been traversed in this way, use'displayPolygonOnDrawable'.


2. Problem is that this says nothing about the colour in which to draw theface. This can be easily rectified:
• Add a new entry to the Face data structure, and a corresponding function:
• Before actually drawing the polygon call setColourOnDrawable(face->red,face->green, face->blue).


3. To implement 'displayObject', run through all faces in the object calling'displayFace'.

Back Face Elimination

For any polyhedral object obviously not all of its faces can be simultaneouslyvisible from any viewpoint. The kind of parallel projection we have definedis equivalent to looking on a line of sight down the positive Z axis, towardsthe origin (from infinitely far away).

Back face elimination involves displaying only those polygons that arefacing towards the viewpoint. Here is where we can make use of theplane equation of a face. Suppose the plane equation is l(x,y,z) = ax +by + cz -d = 0. Then we know that l(X,Y,Z) > 0 when (X,Y,Z) is 'in frontof' the polygon, ie, the polygon is facing towards (X,Y,Z).

So suppose (0,0,Z) (Z>0) is a point on the Z axis. Then, l(0,0,Z) =cZ - d. We require this to be >0 for a visible face. Ie, cZ - d > 0, andhence d < cZ.

Z is arbitrarily large for a parallel projection (it is at 'infinity').So the requirement d < cZ is equivalent to:

if c > 0 then d can be anything (since d < cZ = +infinity is certainlytrue).
if c < 0 then d must be < -infinity (impossible).
if c = 0 then d must be negative.

Hence the requirement is:
display the face which has plane equation parameters (a,b,c,d) if andonly if c > 0 or (c 0 and d < 0).

Loading objects from file

You now need to write a new constructor for GObject which extendsthe present constructor to read in data from a file according to the specified format below. If you are not sure how to go about doing this, please ask the lab assistant

The format is decribed here for a simple object. We are interested in loading a cube and a pyramid.

Note: colour information has been added, but assuming that you use amonochrome machine only, or only care about displaying as wire frame, thisis not necessary. The colours given are suggested only, use whatever youlike.

Test Program

A sample test program (ShowParallel.java) is available (and at /import/teaching/BSc/CG/lib-java). Please note that there are some small bugs in the code that will need fixing. If you can't fix it, please ask the TAs or your fellow students for advice.

Display a parallel projection of the CUBE AND PYRAMID objects (assuming a plan view lookingdown the positive Z axis, towards the origin - hence (x,y,z) projects to(x,y). Style works 2000 serial number search. Such is the nature of orthographic parallel projection, this will bea rather boring view (you should see a square and an triangle).

To make it more interesting, rotate the cube and pyramid about the Yaxis (transformVerticesOfObject) eg, by 30 degrees(pi/6), clear the window and redisplay. Keep doing this, say 12 times,so that the objects should have rotated a full 360 degrees. Betweeneach rotation, clear the display ('clearDrawable') .Important note: when you rotate the vertices of an object, obviouslythe old plane equations are no longer valid. So the transformation functionsshould take this into account.

A working implementation of test program represents a point of assessmentin the coursework.