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• Parametric representation f (u) = (x(u), y (u), z (u)) Coordinates expressed in terms of one independent variable, the parameter. ECS 175 Chapter 3: Object Representation 46 Parametric Representation
• Set of control points
• Piecewise linear representation vs. higherorder parametric curves Linear representation
Linear interpolation ECS 175 Chapter 3: Object Representation Bézier curve (cubic)
Approximation 47 Bézier Curves
• Relaxing the interpolation condition allows for more stable curve construction (approximation)
• Goals:
• Easy construction
• Suitable for rendering and basic geometric operations
• Control over smoothness
• Stability
• Easy computation of derivatives ECS 175 Chapter 3: Object Representation 48 Bézier Curves
• Geometric construction of a cubic Bézier curve Four control points are weighted to construct a cubic Bézier curve.
ECS 175 Chapter 3: Object Representation 49 Bézier Curves
• Bézier curve constructed by repeated linear interpolation f ( u) = n
bin (u)pi curve blends together control po...
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 Spring '08
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