Algorithm in SimplexNumerica

Curve and surface algorithm are important topics in SimplexNumerica for geometric modelling and visualization courses. The Algorithm functions in SimplexNumerica, especially the Interpolation and Approximation algorithm providing another level of sophistication.

In many situations such as surface re-engineering and facial movement animation, you may specify a set of data points that describes a desired shape (e.g., surface model) through any probing or scanning, and obtain a surface that contains all data points. Interpolation is also important in computer animation. An animator may specify a number of key camera positions and orientations (i.e., key frames), interpolate these positions with any Spline curve (i.e., camera path), and interpolate the key frames with additional frames. While interpolation can produce a curve/surface that follows the shape of the data points, it may oscillate or wiggle its way through every point. Approximation can overcome this problem so that the curve/surface still captures the shape of the data points without containing all of them.

SimplexNumerica provides the following algorithm:

Shows you where you can find and how to call the algorithm.

Plotting formulas inside a chart.

Shows you how you can use the Smith diagram in SimplexNumerica and the algorithm behind.

- Linear Least Squares Fit
- Exponential Least Squares Fit
- Logarithmic Least Squares Fit
- Power Least Squares Fit
- Inverse Least Squares Fit
- n-dimensional Polynomial
- Quadratic Polynomial
- Cubic Polynomial
- Sine Wave

- Simplex Algorithm Fit
- Gauß Algorithm Fit
- Bezier
- B-Spline
- Smoothing Spline
- Parametric Smoothing Spline
- Cyclic Smoothing Spline

- Polygonal Curve
- Additive Segmentation
- (n-1) Polynomial
- Lagrange polynomial
- Newton Polynomial
- Rationale Polynomial
- Aitken/Neville Polynomial
- Cubic Spline
- Parametric Spline
- Periodic Spline
- Cyclic Spline
- Smooth Spline
- Akima Subspline
- Renner Subspline
- Hermite Splines
- Catmull-Rom Spline
- Kochanek-Bartel Spline
- Cardinal Spline

- Bi-Linear
- Nearest Neighbors Linear
- Smoothing Spline
- Thin Plate Surface Spline
- Nearest Neighbors Distance
- Nearest Neighbors Around Distance
- Thin Plate Surface Spline
- Bivariate Cubic Spline

- Approximation
- Spectrum
- Phase
- Analysis
- Synthesis
- Real Part
- Imaginary Part

- Auto Detection
- Dean-Dixon
- Nalimov
- Grubbs
- Significance of extreme values
- Outlier Table
- Show Outlier Test Limit
- Show Outliers in Output Window
- Acoustics Alarm if any Outlier

- Hull Edge Points
- Hull Polygon
- Hull Curve

- Routine from MIR (Russian Space Station)
- Removing nth Data Points
- Polyline Simplification
- Radial Vertex Reduction
- Perpendicular Vertex Reduction
- Retake Perpendicular Vertex Reduction
- Reumann/Witkam Reduction
- Ramer/Douglas/Peucker Reduction
- Optimized Ramer/Douglas/Peucker Reduction
- Opheim Simplification

- Add Array
- Add Number
- Sub Array
- Sub Number
- Mul Array
- Mul Number
- Div Array
- Div Number
- Abs