PPT6: Advanced Geometric Algorithms CAP 6736 Geometric Modeling PPT6: Advanced Geometric Algorithms PPT and video are due no later than February 22 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

Point Projection Suggested content: Point projection to curves Math a basic algorithm

Point Projection Suggested content: Point projection to curves Conditions for convergence

Point Projection Suggested content: Point projection to surfaces Math a basic algorithm

Point Projection Suggested content: Point projection to curves Conditions for convergence

Surface Tangent Vector Inversion Suggested content: Surface tangent inversion Math a basic algorithm

Projection of Curves Suggested content: Project curves to planes Parallel case: projected control points

Projection of Curves Suggested content: Project curves to planes Perspective case projected control points new weights

Projection of Surfaces Suggested content: Project surfaces to planes Parallel and perspective cases

Transformations Suggested content: Transformation of curves and surfaces rotation, scaling, shear translation projections

Reparametrization Suggested content: Reparametrization of curves General formula A detailed example

Reparametrization Example Suggested content: Reparametrization example of Bezier Use derivatives to compute control points

Linear Parametrization Function Suggested content: Reparametrization example: linear functions

Reparametrization of NURBS Curves Suggested content: Reparametrization of NURBS curves General formula Algorithm sketch

Reparametrization of NURBS Curves Suggested content: Reparametrization examples Use different functions

Better Circle Weights Suggested content: Better circle weights using reparametrization

Reparametrization with Linear Rationals Suggested content: Reparametrization with linear rational functions General formula and algorithm sketch

Reparametrization with Linear Rationals Suggested content: Reparametrization curve examples Reparametrization surface examples

Making End Weights Equal Suggested content: Making end weights as reparametrization

Curve Reversal Suggested content: Curve reversal as reparametrization

Surface Reversal Suggested content: Surface reversal as reparametrization

B-spline to Power Basis Conversion Suggested content: B-spline curve to power basis conversion decompose into Bezier convert Bezier reparametrize to power basis

B-spline to Power Basis Conversion Suggested content: B-spline surface to power basis conversion decompose into Bezier convert Bezier reparametrize to power basis

Power Basis to B-spline Suggested content: Power basis to B-spline curve conversion reparametrize power basis segments convert power basis to Bezier form B-spline from Bezier remove excess knots

Power Basis to B-spline Suggested content: Power basis to B-spline surface conversion reparametrize power basis segments convert power basis to Bezier form B-spline from Bezier remove excess knots

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: Use point projection to curves and surfaces Find interesting applications