modeling techniques

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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