0.2 Graphic composition in processing  (Page 7/8)

Pills of opengl

OpenGL is a set of functions that allow the programmer to access the graphicsystem. Technically speaking, it is an Application Programming Interface (API) . Its main scope is the graphic rendering of a scene populated by 3D objects and lights, from a givenviewpoint. As far as the programmer is concerned, OpenGL allows to describe geometric objects and some of their properties, andto decide how such objects have to be illuminated and seen. As far as the implementation is concerned, OpenGL is based on the graphic pipeline , made of modules as reported in [link] . An excellent book on interactive graphics in OpenGL was written by Angel .

The opengl pipeline

In Processing (and in OpenGL), the programmer specifies the objects by means of world coordinates( standard coordinates ). The model-view matrix is the transformation matrix used to go from standard coordinates to a spaceassociated with the camera. This allows to change the camera viewpoint and orientation dynamically. In OpenGL this is donewith the function gluLookAt() , which is reproduced in Processing by the camera() . The first triple of parameters identifies the position, in worldcoordinates, of the optical center of the camera ( eye point ). The second triple of parameters identifies a point where the camera is looking at ( center of the scene ). The third triple of coordinates identifies a vector aimed at specifying the viewing vertical. For example,the program void setup() {size(100, 100, P3D); noFill();frameRate(20); }void draw() { background(204);camera(70.0, 35.0, 120.0, 50.0, 50.0, 0.0, (float)mouseX /width, (float)mouseY /height, 0.0);translate(50, 50, 0); rotateX(-PI/6);rotateY(PI/3); box(45);} draws the wireframe of a cube and enables the dynamic rotation of the camera.

The projection matrix is responsible for the projection on the viewing window, and this projection canbe either parallel (orthographic) or perspective. The orthographic projection can be activated with the call ortho() . The perspective projection is the default one, but it can be explicitly activated with the call perspective() . Particular projections, such as the oblique ones, can be obtained by distortion of objects byapplication of the applyMatrix() . There is also the texture matrix , but textures are treated in another module.

For each type of matrix, OpenGL keeps a stack, the current matrix being on top. The stack data structure allows to savethe state (by the pushMatrix() ) before performing new transformations, or to remove the current state andactivate previous states (by the popMatrix() ). This is reflected in the Processing operations described in [link] . In OpenGL, the transformations are applied according to the sequence

1. Push on the stack;
2. Apply all desired transformations by multiplying by thestack-top matrix;
3. Draw the object (affected by transformations);
4. Pop from the stack.