Exercise 1: For smooth shading of polygon meshes, the so-called vertex normals are needed. Suppose three triangles share

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Exercise 1: For smooth shading of polygon meshes, the so-called
vertex normals are needed. Suppose three triangles shares a vertex
v and that the normals of these triangles are: n = -4 [3.-4,0] [
-4,0,3] ng = [0,1,2] n2 = = Calculate a suitable vertex normal for
v.
answer for Exercise 1:
To calculate the vertex normal v, we have to cross-product the
normal vectors of the sides of the triangles.
So vertex1 = n2 - n1, vertex2 = n3 - n1
vertex1 = (-4-3,0-(-4),3-0) = (-7,4,3)
vertex2 = (0-3,1-(-4),2-0) = (-3,5,2)
Now cross product of the vector1 x vector2

Exercise 1 For Smooth Shading Of Polygon Meshes The So Called Vertex Normals Are Needed Suppose Three Triangles Share 1 (15.03 KiB) Viewed 20 times

So the normal vector v =
(-7,5,-23) with the magnitude
= 24.55

Exercise 1 For Smooth Shading Of Polygon Meshes The So Called Vertex Normals Are Needed Suppose Three Triangles Share 2 (31.84 KiB) Viewed 20 times

і k ax b = 1 i k ar ay а, bx by -7 4 3 = i (4:2 - 3.5) - ) ((-7).2 - 3•(-3)) + k((-7),5 - 4•(-3)) = ? (8 - 15)-3(-14 +9)+k(-35+ 12) = {-7; 5; -23} -3 5 2

Exercise 2: Find the intensity at the surface point p = (1.5,4.2) with normal N = [3.2,-2.2] by using the Phong illumination model. Assume the following parameters: a point light source located at 9 = (5.4.5.3), an eye position e = (3.3, 3.9), a Phong exponent a = 8, and diffuse and specular reflection constants are ka = 0.64 and ks = 0.81, respectively. Note: ignore the ambient term and assume the light source has maximum intensity.