This assignment is due by the start of class on Wed., Oct. 4.  Please put your name, name of program, and compiling instructions at the top of your files. In addition, describe the features you've implemented and comment each function (explaining briefly what it does and what its arguments are).  You should provide sufficient additional comments for the graders to understand the logic of the program. 

  The objective of the assignments for the next 2.5 weeks is to implement a graphics pipeline that draws a polygon mesh entered by the user. For the first part of the assignment we will focus on constructing the pipeline for a single polygon. You will read in a polygon represented by vertices in 2D model coordinates. You should convert each vertex to 3D homogenous model coordinates. (Situate the polygon in the z=0 plane.) When the users asks that the polygon be drawn you should process the vertices through the graphics pipeline.

  The steps of the pipeline are:

• Transform each vertex of the polygon to world coordinate; i.e. multiply it by the current transformation matrix.
• Clip the world-coordinate vertices to the current viewing volume. For the current assignment you need only worry about orthographic projection with the viewing volume bounded by the planes x=-250, x=250, y=-250, y=250, z=250, and z=-250, where far is specified by the user.
• Project the clipped vertices into the projection plan; i.e. multiply it by the current projection matrix.
• Scan convert the polygon defined by the projected vertices; i.e. use your polygon filling routine from the last assignment. Note you should not outline the polygon nor draw its vertices; just fill it.

• You should define (at least) two classes (or structs if you are programming in C) for this assignment.
  • The class vertex contains four floats xCoord, yCoord, zCoord, and wCoord.
  • The class polygon contains four vertex arrays to store the vertices of the polygon in the various coordinate systems: ModelVertices, WorldVertices, ClipVertices, and ProjectedVertices. We will limit the number of allowable vertices per polygon to 20 so, to simplify your task, you can used fixed-size arrays. The class should also contain the number of vertices in the original model, the number of vertices in the clipped version (which may be less), and the polygon color.
  You may, of course, add any additional information you find useful.
• You should implement the following routines.
  • LoadIdentity(float* M) which initializes a 4X4 matrix of floats to the indentity matrix.
  • Three transformation routines: translate(float dx, float dy, float dz), scale(float sx, float sy, float sz), rotate(float angle, axis rotationaxis). Each modifies the current transformation matrix, which is a global 4X4 matrix of floats called CTM.
    • Translate computes the transformation matrix M to translate by (dx,dy,dz) and then sets CTM=CTM*M.
    • Scale computes the transformation matrix M to scale by (sx,sy,sz) and sets CTM=CTM*M.
    • Rotate computes the transformation matrix M to rotate "angle" degrees about "rotationaxis" (where axis is defined: enum axis {xaxis, yaxis, zaxis}). It then sets CTM=CTM*M. The user will input the angle in degrees but be sure to convert to radians before calling the cos/sin functions.
  • A 3D polygon clipping routine int polyClip(vertex* vertexlist). When in orthographic projection mode the routine clips the polygon defined by vertexlist to the standard viewing volume, i.e. the region bounded by the planes x=-250, x=250, y=-250, y=250, z=0, and z=far. The routine overwrites vertexlist with the clipped vertices and returns the number of vertices in the clipped polygon. If you are using C++ you may want to make this a member function of the polygon class (in which case you don't need to pass it vertexlist).
  • A projection routine void Ortho() that sets the current projection matrix for orthographic projection. The current projection matrix is a global variable called CPM.
  The file hw3.cpp has the user interface and some routines for matrix/vector arithmetic. It has several "hooks" where you should insert your code.