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CS 405/805-001: Computer Graphics Assignment 2

 Assignment 2

CS 405/805-001: Computer Graphics
 
In this assignment, you are to implement a simple ray-tracing algorithm outlined 
below:
main ()
{
Initialize the global data structures;
for (i=0; i
for (j=0; j
Construct the ray, V, started from the CenterOfProjection, P0,
and passing through the pixel (i, j);
if ((c = ray-tracing( P0, V ) != nil) // if the ray 
// intersects with an object
image[i][j] = c; // save the returned shading
// value into the image buffer.
}
Output the final image;
}int ray-tracing( P0, V ) {
// If the ray intersects with any object, this function call will
// return a true value, and the data of the intersection are return
// in P, N, and kd.
found = ray-objects-intersection( P0, V, P, N, kd );
If (found) {
C = shading( P, N, kd );
return ( C );
} else
return( nil );
}
The main computations are in the following three functions:
// Construction of ray
// Input: pixel index (i, j) in the screen coordinates
// Output: P0, V0 (for parametric ray equation P = P0 + V0*t)
// in the world coordinates.
void ray_construction(int i, int j, float P0[3], float V0[3])
{
// Step 1:
// Map (j, i) in the screen coordinates to (xc, yc) in the
// camera coordinates.
// Step 2:
// Transform the origin (0.0, 0.0, 0.0) of the camera
// coordinates to P0 in the world coordinates using the
// transformation matrix Mcw. Note that the transformed result
// should be VRP.
// Step 3:
// Transform the point (xc, yc, f) on the impage plane in
// the camera coordinates to P1 in the world coordinates using
// the transformation matrix Mcw.
// V0 = P1 – P0;
// normalize V0 into unit length;
return;
}
// Ray-Object Intersection
// Input: ray – P0, V0
// Output: the nearest intersection point P[3] if found, along with
// N[3], the surface normal at that point, and
// kd, the diffuse reflection coefficient of the surface.
// Note: In a general system, the objects should be stored a list
// structure. A loop will scan through each object in the list. The
// nearest intersection point is found. In our case, we will have only
// two hard-coded objects: a sphere and a polygon.
// So, this part is “hard-coded” for now.
int ray_object_intersection(float P0[3], float V0[3],
float P[3], float N[3], float kd) {
t1 = ray-sphere-intersection(float P0[3], float V0[3],
struct sphere S, float N1[3], float kd1);
t2 = ray-polygon-intersection(float P0[3], float V0[3],
struct polygon PL, float N2[3], float kd2);
if (t1 == nil and t2 == nil)
return nil;
else if (t2 == nil) {
P = P0 + t1*V0;
N = N1;
Kd = kd1;
return 1;
} else if (t1 == nil){
P = P0 + t2*V0;
N = N2;
Kd = kd2;
return 1;
} else if (t1 < t2){
P = P0 + t1*V0;
N = N1;
Kd = kd1;
return 1;
} else {
P = P0 + t2*V0;
N = N2;
Kd = kd2;
return 1; } }
// Shading:
// Input: P[3] – point position
// N[3] – surface normal at that point
// kd – diffuse reflection coefficient of the surface
// Output: C – shading value
int shading(float P[3], float N[3], float kd)
{
L = LRP – P; // LRP is the light position
normalize L to unit length;
C = Ip * kd * (N * L); // where (N * L) is dot-product
}
Global Data Structure:
It includes, but not limited to the followings:
 The cameral model – VRP, VPN, VUP
 The light position – LRP
 The transformation matrices: Mwc, Mcw
 Image buffer image[ROWS][COLS];
Input Model:
Ideally, all objects should be defined in a script data file. In the initialization stage, 
the objects are read into the program and stored in a list structure. In this 
assignment, we will have only two objects – a sphere and a polygon. To simplify
this part of processing, you are allowed to hard-code the objects, together with 
the global data structure into a header file (e.g. “model.h”).
The camera model and light information are usually also specified in the input 
script file. You are also allowed to hard-code them in the header file. However, 
the transformation matrices Mwc and Mcw should computed in the initialization 
stage.
I will provide a sample “model.h” file. You should test your program with this data 
file.
You are then required to:
 Modify the camera model in the “model.h” to generate a picture from a 
different view; and
 Modify the polygon position in the “model.h” to generate a picture with a 
slightly different scene.
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