Class 3: Curves and surfaces

Curves

• concept of a 'curve'
• straight vs. segmented vs. curved (!) curves
• 2D vs 3D curves
• tangent
• normal
• binormal
• curvature
• Frenet frame
• torsion - for space curves
• parabola
• parametric curves
• circle
• Spirograph
• spirals
• tangent discontinuities (cusps)
• asteroid
• cardioid
• knots
• spirolaterals
• DCP
• Lissajous curves
• fractal curves - Koch, Sierpinski, Hilbert

Surfaces

• parametric form
• computing surfaces as polymeshes
• Eg. Boy's surface
• minimal surfaces
• http://mathworld.wolfram.com/topics/MinimalSurfaces.html
• tgt. plane (u,v), normal - UVN system
• curvature: http://www.google.com/search?hl=en&q=curvature+mathworld&btnG=Google+Search
• universal shape equation: http://astronomy.swin.edu.au/~pbourke/surfaces/supershape3d/
• 'catastrophe theory' - surface discontinuities: http://en.wikipedia.org/wiki/Catastrophe_theory