CSCE 441 Lecture 40

« previous | Tuesday, April 29, 2014 | next »

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
• $\left|n_0\right|=\left|n_1\right|=|n(t)|$
• $n(t)=\alpha n_0+\beta n_1$
• $\begin{array}{rlrl}{n}_0\times n(t)& =n_0\times (\alpha n_0+\beta n_1)& n_1\times n(t)& =n_1\times (\alpha n_0+\beta n_1)\\ & =\beta (n_0\times n_1)& & =\alpha (n_1\times n_0)\\ |n_0\times n(t)|& =\beta |n_0\times n_1|& |n_1\times n(t)|& =\alpha |n_1\times n_0|\\ \left|n_0\right||n(t)|\sin (\theta t)& =\beta \left|n_0\right|\left|n_1\right|\sin \theta & \left|n_1\right||n(t)|\sin (\theta (1-t))& =\alpha \left|n_1\right|\left|n_0\right|\sin \theta \\ \sin (\theta t)& =\beta \sin \theta & \sin (\theta (1-t))& =\alpha \sin \theta \\ \beta & =\frac{\sin (\theta t)}{\sin \theta }& \alpha & =\frac{\sin (\theta (1-t))}{\sin \theta }\\ \end{array}$
• $n(t)=\frac{\sin (\theta (1-t))n_0+\sin (\theta t)n_1}{\sin \theta }$