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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} between origin and endpoints
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left| n_0 \right| = \left| n_1 \right| = \left| n(t) \right|}
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n(t) = \alpha \, n_0 + \beta \, n_1}
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} 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{align}}
• $n(t)={\frac {\sin {(\theta \,(1-t))}\,n_{0}+\sin {(\theta \,t)}\,n_{1}}{\sin {\theta }}}$