CIS681 Lab 5

Objective

Assignment

• Call your program lab5.

• As before, your program should take an argument of a scene description file. Add a command for triangulated objects that includes a radius for a bounding sphere in order to speed up execution of your program. We will use the convention that the vertices of a face are ordered in a clockwise direction when the face is viewed from the front (the outside side of the face).

  triangles <radius> <number of vertices, n>  <number of faces, m>
  
  x1 y1 z1
  x2 y2 z2
  ...
  xn yn zn
  
  v11 v12 v13
  v21 v22 v23
  ...
  vm1 vm2 vm3
  
  r g b 
  kd ks n 
  kt n1
  

  See the sample tetrahedron, cone, and cuboid

• As before, the execution of your program should produce a .ppm file specified in the scene description file.

• As before, your lab will be graded under UNIX using the following (assuming the scene description file is called input.txt and the corresponding .ppm file is called output.ppm):

  make
  lab5 input.txt
  convert output.ppm output.jpg
  display
  

• Implement Phong smooth shading using barycentric coordinates

• Include with your submission one or more input files showing transformed, including non-uniform scale, convex triangulated polyhedra. You can use the ones linked to off of this page or you can make your own - but be careful to keep the clockwise orientation of the vertices defining the face. Input scene description files should show multiple objects (at least 4) including the cubiod (or something of equal complexity) and tetrahedron. You can also include cubes and spheres in the scene.

• You do need to do shadows when rendering the polygonal models; you do not need to include reflection, refraction, or texture mapping, but interesting images that contain such things might garner extra credit.

Notes

• The combination of a vertex list that contains coordinate values and a face list that indexes into the vertex list is a common but simple data structure to keep an object description.

  Read in the triangle command and, besides recording radius, color, and the illumination parameters, make the following lists:

  • vertex list: this is a list of the object's x,y,z coordinates
  • face list: this can be as simple as a one-dimensional list of integer indices. In that case, the vertices of face i are:

    vertex_list[face_list[i*3]]
    vertex_list[face_list[i*3+1]]
    vertex_list[face_list[i*3+2]] 
    

  • face normal list: this contains, for each face, a normalized cross product of 2 edges from the face, ordered so the normal (the result of the cross product) points outward.
  • d list: this is a list of constants completing the planar equation of each face, using the face normal, N, just computed and a point on the plane, P, (e.g. one of the vertices of the face): P.N = d.
  • vertex normal list: see note below.

• After computing a normalized normal for each face, you need to compute a normalized normal for each vertex:

  For each vertex, i
    vertex_normal[i] = (0,0,0)
  For each face, j
    For each vertex k of face j
      vertex_normal[k] += face_normal[j]
  For each vertex, i
    normalize vertex_normal[i]
  

• Computing the intersection with the convex triangulated polyhedron is the same logic as the cube from Lab #4. The difference is that, here, you are dealing with arbitrary planar equations and an arbitrary number of planes, but it's the same procedure for determining the maximum entering t-value that is less than the minumum exiting t-value.

• For Phong smooth shading, compute the barycentric coordinates of the intersection point and use those to average the vertex normals to produce a normal for the intersection point.
  • The barycentric coordinates of the intersection point defines the point by a weighted average of the 3 triangle vertices. To generate barycentric coordinates of the intersection point, P, compute areas a, b, and c of the sub-triangles P-V1-V2, P-V2-V3, and P-V3-V1, respectively. Each triangle vertex is weighted by the relative area of the opposite sub-triangle so that P = (a*V3 + b*V1 + c*V2)/(a+b+c).

  • The areas of the sub-triangles are computed by:

    a = 0.5*|(P-V1)x(V2-V1)|
    b = 0.5*|(P-V2)x(V3-V2)|
    c = 0.5*|(P-V3)x(V1-V3)|
    

  • Use the barycentric coordinates as weights to interpolate the vertex normals:

    object_space_normal = (a*NV3 + b*NV1 + c*NV2)/(a+b+c)
    

  • Notice that you really don't need to include the 0.5 factor in the area calculation because it just gets divided out by the normalizing division of a+b+c.

Extra Credit - to receive extra credit, include a README.txt file explaining any extra credit you've done along with input files demonstrating that extra credit.

• Process concave triangulated polyhedra. After computing the ray-plane intersection point, you need to test whether it is inside of the triangle or not. The other change to make is that if a ray is outside of the plane of a face (the source is on the outside side of the plane and the ray direction is either parallel to the plane or points away from it), you still need to continue processing faces because it still may intersect the concave object.
• Create a scene that incorporates reflection, refraction, and/or texture mapping along with smooth shaded polyhedra in interesting ways.
• In the input file, include u,v coordinates along with the vertex x,y,z coordinates to map the vertices into a surface texture space. Interpolate these u,v values just like you interpolate the normal using barycentric coordinates. Apply a surface texture to the polyhedron using the interpolated u,v coordinates.