CSCE 441 Lecture 40

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End Exam 2 content

Final Exam Review

Shadows, Collision Detection, Programmable Shaders, Quaternions, and Antialiasing will not be on the final.

Subjects:

• Shading / Texturing
• Hidden Surfaces
• Ray Tracing
• 3D Geometry
• Radiosity
  • BRDF
• Solid Modeling
• Smooth Curves
• Smooth Surfaces
• Topics covered by assignments

Cumulative final, but less likely to ask questions that were asked on the midterm.

No code.

Interpolation of Normals

Linear interpolation:

• origin to point on straight line between two points

Spherical linear interpolation

• interpolate over angle $\theta$ between origin and endpoints
• $\left|n_{0}\right|=\left|n_{1}\right|=\left|n(t)\right|$
• $n(t)=\alpha \,n_{0}+\beta \,n_{1}$
• ${\begin{aligned}n_{0}\times n(t)&=n_{0}\times \left(\alpha \,n_{0}+\beta \,n_{1}\right)&n_{1}\times n(t)&=n_{1}\times \left(\alpha \,n_{0}+\beta \,n_{1}\right)\\&=\beta \,\left(n_{0}\times n_{1}\right)&&=\alpha \,\left(n_{1}\times n_{0}\right)\\\left|n_{0}\times n(t)\right|&=\beta \,\left|n_{0}\times n_{1}\right|&\left|n_{1}\times n(t)\right|&=\alpha \,\left|n_{1}\times n_{0}\right|\\\left|n_{0}\right|\,\left|n(t)\right|\,\sin {(\theta \,t)}&=\beta \,\left|n_{0}\right|\,\left|n_{1}\right|\,\sin {\theta }&\left|n_{1}\right|\,\left|n(t)\right|\,\sin {(\theta \,(1-t))}&=\alpha \,\left|n_{1}\right|\,\left|n_{0}\right|\,\sin {\theta }\\\sin {(\theta \,t)}&=\beta \,\sin {\theta }&\sin {(\theta \,(1-t))}&=\alpha \,\sin {\theta }\\\beta &={\frac {\sin {(\theta \,t)}}{\sin {\theta }}}&\alpha &={\frac {\sin {(\theta \,(1-t))}}{\sin {\theta }}}\\\end{aligned}}$
• $n(t)={\frac {\sin {(\theta \,(1-t))}\,n_{0}+\sin {(\theta \,t)}\,n_{1}}{\sin {\theta }}}$