• Differential Geometry of Surfaces
• Jordan Smith
• UC Berkeley
• CS284
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Differential Geometry of a Curve
• Differential Geometry of a Curve
• Differential Geometry of a Curve
• Differential Geometry of a Curve
• Differential Geometry of a Curve
• Differential Geometry of a Curve
• Computing the Curvature of a Curve
• Computing the Curvature of a Curve
• Computing the Curvature of a Curve
• Computing the Curvature of a Curve
• Computing the Curvature of a Curve
• Computing the Curvature of a Curve
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• First Fundamental Form IS
• Metric of the surface S
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Differential Geometry of a Surface
• Second Fundamental Form IIS
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Change of Coordinates
• Change of Coordinates
• Change of Coordinates
• Change of Coordinates
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Curvature
• Curvature
• Curvature
• Curvature
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Weingarten Operator
• Weingarten Operator
• Weingarten Operator
• Outline
• Differential Geometry of a Curve
• Differential Geometry of a Surface
– I and II Fundamental Forms
– Change of Coordinates (Tensor Calculus)
– Curvature
– Weingarten Operator
– Bending Energy
• Bending Energy
• Bending Energy
• Conclusion
• Curvature of Curves and Surfaces
• Computing Surface Curvature using the Weingarten Operator
• Minimizing Bending Energy
– Gauss-Bonnet Theorem
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