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A CS 4620 Midterm Exam from Cornell University. The exam consists of several questions related to computer graphics, including meshes, cube maps, transformation stacks, and normal interpolation. The exam also includes a statement on academic integrity. a buffer of vertex positions and normals, as well as an index buffer for a given mesh structure.
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This 90-minute exam has ?? questions worth a total of ?? points. Use the back of the pages if you need more space.
Academic Integrity is expected of all students of Cornell University at all times, whether in the presence or absence of members of the faculty. Understanding this, I declare I shall not give, use, or receive unauthorized aid in this examination.
Signature: Date
-1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.2, 0.0, 0.0, -0.2, 0.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.
We are also given the following normal buffer:
-5/13, 0.0, 12/13, 0.0, 5/13, 12/13, 0.0, 8/17, 15/17, 0.0, -8/17, 15/17, 0.0, -5/13, 12/13, 5/13, 0.0, 12/
Finally, we also have an index buffer. Each grouping of 3 entries describes a single triangle in the original mesh. An entry with value i selects the ith point in the position buffer above, and the ith vector in the normal buffer above. 0, 2, 1, 0, 3, 2, 0, 4, 3, 1, 2, 5, 2, 3, 5, 3, 4, 5
Figure 1: Left: the original mesh structure, with the edge to be removed highlighted in red. Note that this mesh is planar. Right: the resulting mesh structure.
Similar to the written question in A4 shaders, imagine we have a cube map with cross-like texture, shown in the figure below.
Figure 2: cube map with cross like texture.
Suppose we have a perspective camera positioned at (0, 0 , −25) looking towards (0, 0 , 0). A square mirror surface 100 by 100 units in size is centered at (0, 0 , 0) with its normal pointing towards −z. The scene is rendered using the cube map as an environment map.
(a) Explain why we want to interpolate vertex normals for shading.
(b) True or False? For any point on a face ABC, the normal we use for shading is a convex linear combination of the vertex normal vectors na, nb, and nc.^1
(c) Suppose we have a triangle mesh with shared vertex normals, which contains two triangles P QR and RQS that share an edge. What are the barycentric coordinates of the midpoint of the edge QR in each of these two triangles?
(d) Prove using barycentric coordinates that the interpolated normal at any point on the edge QR has the same value when calculated in triangle P QR using the vertex normals np, nq, and nr or in triangle RQS using the vertex normals nr, nq, and ns.
(^1) Reminder: a convex linear combination is a linear combination in which the weights are positive and sum to 1.
The image here is a correct ray traced rendering of a scene consisting of a single light, a box, a teapot mesh, a sphere, and a plane (approximated by a box with a small height). The teapot has Microfacet Beckmann shading, and all other surfaces have Lambertian. We have modified the ray tracer to introduce several single-line bugs, one for each image you see on the next page. For each image, choose one of the three possible explanations for the bug:
For each choice, back it up with an example of an error that would cause the observed symptoms. There is no right or wrong explanation; only plausible and implausible ones. But when there is a clearly plausible cause, very far-fetched explanations will not make full credit. Shadow computations and texture operations count as part of shading. Computing surface normals counts as part of ray intersection. The first one is done as an example.
(a) Example: Bug ii: Ray intersection is not properly determining the first object hit.
(b)
(c)
(d)
