splines - CS148: Introduction to Computer Graphics and...

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Page 1 CS148: Introduction to Computer Graphics and Imaging Splines and Curves CS148 Lecture 9 Pat Hanrahan, Winter 2009 Topics Splines ± Cubic Hermite interpolation ± Matrix representation of cubic polynomials ± Catmull-Rom interpolation Curves ± Bezier curve ± Chaiken’s subdivision algorithm ± Properties of Bezier curves
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Page 2 Cubic Hermite Interpolation CS148 Lecture 9 Pat Hanrahan, Winter 2009 Cubic Hermite Interpolation Given: values and derivatives at 2 points
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Page 3 CS148 Lecture 9 Pat Hanrahan, Winter 2009 Assume cubic polynomial Solve for coefficients: Cubic Hermite Interpolation CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation
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Page 4 CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation Inverse CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation
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Page 5 CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation of Polynomials CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation of Polynomials
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CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation of Polynomials CS148 Lecture 9 Pat Hanrahan, Winter 2009 Matrix Representation Transpose
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splines - CS148: Introduction to Computer Graphics and...

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