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Modeling Techniques

Dan, Phoenix, Carl. Modeling Techniques. Several ways you can model Polynomial functions, linear functions, splines. General Modeling. Linear interpolation. Red is the approximation. Polynomial interpolation. Red is the approximation. Spline interpolation. Red is the approximation.

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Modeling Techniques

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  1. Dan, Phoenix, Carl Modeling Techniques

  2. Several ways you can model • Polynomial functions, linear functions, splines General Modeling

  3. Linear interpolation Red is the approximation

  4. Polynomial interpolation Red is the approximation

  5. Spline interpolation Red is the approximation

  6. Pugh Analysis Using the HP 6-coefficient polynomial as a baseline

  7. Visual Comparison From “Fast B-Spline Transforms for Continuous Image Representation and Interpolation” Unser, et al.

  8. Used when enlarging images Fast Less accurate Bilinear Interpolation

  9. Used by HP for their PTMs • They recommended this in 2001 in their paper “Polynomial Texture Maps” • Do not specify why 6 Coefficient Biquadratic Polynomial

  10. Piecewise cubic functions to model high order polynomials Eliminates Runge’s phenomenon LabVIEW has a VI for it! B-Spline

  11. back The red curve is the Runge function.The blue curve is a 5th-order interpolating polynomial (using six equally-spaced interpolating points).The green curve is a 9th-order interpolating polynomial(using ten equally-spaced interpolating points).

  12. Piecewise functions The spline is made up of pieces of the cubic functions shown above. The bolded sections show which pieces are used. back

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