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Quiz solution

Programming Homework

	Drawing pixels. Animation.
	Weight functions.
	Line segments.
	Light.
	Ray casting. Postscript

Creating a spherical emittance distribution

Each team computes z = sqrt(1-x²-y²) on a unit grid. The grid is projected onto cardboard. Using paper with gray levels from 0.0 to 1.0, each team cuts a pixel with color z and attaches it to location (x,y). Each member of the faster team received a souvenir sphere (a ping-pong ball).

Students

Computer graphics is the reason you have learned how to program. Computer graphics is why you want a fast machine. Computer graphics is the microscope, the telescope, the x-ray glasses that let you examine all sorts of objects that are fabricated digitally. Computer graphics gives you your own TV station.

This course is concerned with algorithms for creating 2D images of objects in 3-dimensional space. To make objects that look real, we simulate the way light is emitted from sources and then reflects off surfaces. Representing the shape and reflectance of an object is called modeling. Sampling the shape according to a 2D sampling pattern (dictated by pixels) is called rasterizing. Sampling the view directions is called ray-casting. Computational scattering evaluates the flow of light. In general, graphics algorithms are characterized by their outer loop. An object-order renderer loops over the geometry in 3D. An image-order renderer loops over the rays through a viewpoint. The rest is details.

How they do graphics at other places

Pixar
Stanford
Caltech
UNC Chapel Hill
Georgia Tech
Carnegie Mellon

The Visualization Lab is located in the 4th floor of the Dirac Science Library. It is available for your use weekdays between 8am and 5pm. When using the facility you are a guest of the School of Computational Science and Information Technology. Do not bring food or drinks into the lab.

char G[]="^<VL8CO! ",C[80][80],*P,k,j;double sin(),cos(),c,x,z,L,M,N,i,I=.01;
main(){for(;i<629;){N=sin(i*I);c=cos(i*I);M=sin(i);L=cos(i+=I);x=c+3;z=3*M*x+
60-N;if(z>*(P=&C[k=z+5*N][j=40+x*L*9])){*P=z;c*=L+M-N/c;P[-3200]=G[k=c<0?0:
c*5];}}for(P=*C;P<=C[40];)putchar((P++-*C)%80?*P+32:10);}
  

Unfortunately, it did not win the Obfuscated C Contest.

Here is a small (but slow) triangle renderer I wrote as part of a challenge problem for my computer graphics class in fall 1997. It reads data from stdin, performs linear interpolation and depth-buffering, then writes a .ppm file to stdout. It uses barycentric coordinates. The shortest student-written program that obeyed the contest rules was 100 lines, by Wendong Wang. The shortest student-written program that only cheated a little was 60 lines by Hench Qian (check out the links at the bottom of his page).

I got mine down to 26 lines, no cheating; 11 lines jamming lots of statements per line. Chris Weigle helped me torture it down further to 6 lines.

float V[18],D,b[6];int i,j,k,x=100,I,C;char S[60016];main(){for(C=x*x;read(0,V,
72);)for(j=0;j++<C;){for(I=1,i=18;i;I&=(b[i/6]/=D)>=0)for(i-=6,D=b[i/6]=0,k=3;k+
9;k-=6)D+=k/3*(V[9-k]-*V)*(V[10+k]-V[1]),b[i/6]+=k/3*((V[(i+9-k)%18]-j%x)*(V[(i+
9+k)%18+1]-j/x));if((D=*b*V[2]+b[1]*V[8]+b[2]*V[14])>S[3*C+j]&I)for(i=3;i--;S[3*
C+j]=D)S[j*3+i+15]=*b*V[i+3]+b[1]*V[9+i]+b[2]*V[15+i];}sprintf(S,"P6 %d %d 255 "
,x,x);write(1,S,3*C+15);}
  

When given a list of triangles as input it rendered the image at the upper right.

For a minimal ray tracer, see Paul Heckbert's example.