games101-week6

Curves

Bézier Curves

de Casteljau Algorithm

像是一个枚举所有点的一个算法

Properties of Bézier Curves

Piecewise Bézier Curves

c0 连续是前一段的终点等于后一段的起点

c1 连续是两个控制点共线且离公共点距离一样

Other types of splines

Spline

B-splines

• Short for basis splines
• Require more information than Bezier curves
• Satisfy all important properties that Bézier curves have (i.e. superset)

More Difficult

Surfaces

Bezier surfaces

像编织的方式一样得到的贝塞尔曲面

Mesh Operations: Geometry Processing

Loop Subdivision

Update

Catmull-Clark Subdivision (General Mesh)

Mesh Simplification

Collapsing An Edge

Quadric Error Metrics

Shadow Mapping

Pass 1: Render from Light

Pass 2A: Render from Eye

Pass 2B: Project to light

Visualizing Shadow Mapping

Problems with shadow maps

• Hard shadows (point lights only)

• Quality depends on shadow map resolution (general problem with image-based techniques)

• Involves equality comparison of floating point depth values means issues of scale, bias, tolerance