PPT10: Global and local approximation CAP 6736 Geometric Modeling PPT10: Global and local approximation PPT and video are due no later than March 29 Submit to: lpiegl@gmail.com This template file is just an outline of the presentation that you need to complete. Additional pages may be necessary to fully explore the topic above. Each page should contain adequate text as well as illustrations. You are free to use all publicly available information (text as well as graphics) as long as the sources are properly acknowledged.

Team members’ contributions Member [name]:

Part I: Technical details For this part you will need an equation editor. You may use: MS equation editor, MathType, LaTeX, or Handwritten equations if all else fails

Global Approximation Suggested content: Way-up approach: start with minimum number of control points get approximating curve/surface check the error if deviation is less than the tolerance, done else, increase number of control points and approximate again Way-down approach: start with maximum number of control points if deviation is less than the tolerance, reduce number of control points else, return to previous curve/surface

Least-squares Curve Approximation Suggested content: least-square curve approximation choose parameters and knots compute control points

Least-squares Curve Approximation Suggested content: least-square curve approximation solve matric equation

Least-squares Curve Approximation with end Conditions Suggested content: least-square curve approximation choose parameters and knots compute control points Suggested content: least-square curve approximation with end derivatives choose parameters and knots compute control points

Least-squares Curve Approximation with end Conditions Suggested content: least-square curve approximation set up and solve matrix equation

Least-squares Curve Approximation with end Conditions Suggested content: least-square curve approximation pseudocode algorithm

Least-squares Curve Approximation with end Conditions Suggested content: least-square curve approximation examples with different number of control points

Weighted and Constrained Least Squares Curve Fitting Suggested content: least-square weighted and constraint curve approximation constraint and unconstraint data weights for unconstraint items interpolate constraint data approximate unconstraint data

Weighted and Constrained Least Squares Curve Fitting Suggested content: least-square weighted and constraint curve approximation constraint and unconstraint data setup the matrixes and solve

Weighted and Constrained Least Squares Curve Fitting Suggested content: least-square weighted and constraint curve approximation examples

Least Squares Surface Fitting Suggested content: least-square surface approximation fit curves to rows of data fit curves to rows of control points

Least Squares Surface Fitting Suggested content: least-square surface approximation surface approximation error surface

Least Squares Surface Fitting Suggested content: least-square surface approximation surface approximation error surface

Least Squares Surface Fitting Suggested content: least-square surface approximation data points surface interpolation compared to approximation

Approximation to within a Tolerance Suggested content: curve approximation with error control general strategy error measures

Approximation to within a Tolerance Suggested content: curve approximation with error control examples

Approximation to within a Tolerance Suggested content: surface approximation with error control examples: tolerance = 0.0

Approximation to within a Tolerance Suggested content: surface approximation with error control Examples with different tolerances

Approximation to within a Tolerance Suggested content: curve approximation with data smoothing examples with one and two levels of smoothing

Local Curve Fitting Techniques Suggested content: local curve approximation general quadratic and cubic fitting strategy to find optimal number of arcs

Local Conic Curve Fitting Techniques Suggested content: local conic approximation end tangents and weights

Local Conic Curve Fitting Techniques Suggested content: local conic approximation examples

Local Conic Curve Fitting Techniques Suggested content: local conic approximation examples

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation choice of derivatives constructing of control points non-planar case

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation choice of derivatives constructing of control points planar case

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation error check

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation examples

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation 2D and 3D examples

Local Cubic Curve Fitting Techniques Suggested content: local cubic approximation 3D examples

Part II: Design examples

Design Examples Suggested content: Add design examples: images and/or videos Give credit to the designers

Part III: GM lab For this part of the assignment you may use an existing system, such as Blender, or write the code and visualize the result using graphics tools like Processing.

Geometric Modeling Lab Suggested project: Design shapes using approximation Design common surfaces from point clouds