modeling techniques
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
MODELING TECHNIQUESDan, Phoenix, Carl
GENERAL MODELING Several ways you can model
Polynomial functions, linear functions, splines
LINEAR INTERPOLATION
Red is the approximation
POLYNOMIAL INTERPOLATION
Red is the approximation
SPLINE INTERPOLATION
Red is the approximation
PUGH ANALYSIS
Characteristics B-SplineBilinear
Interpolation6 Coefficient Polynomial
Accuracy + - 0
Speed - + 0
Time needed to learn + 0 0
Recommended + 0 0
Total 2 0 0
Using the HP 6-coefficient polynomial as a baseline
VISUAL COMPARISON
From “Fast B-Spline Transforms for Continuous Image Representation and Interpolation”Unser, et al.
BILINEAR INTERPOLATION Used when enlarging images Fast Less accurate
6 COEFFICIENT BIQUADRATIC POLYNOMIAL
Used by HP for their PTMs
They recommended this in 2001 in their paper “Polynomial Texture Maps” Do not specify why
B-SPLINE Piecewise cubic functions to model high
order polynomials Eliminates Runge’s phenomenon LabVIEW has a VI for it!
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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).
PIECEWISE FUNCTIONS
The spline is made up of pieces of the cubic functions shown above. The bolded sections show which pieces are used.
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