PPT9: Global and local interpolation CAP 6736 Geometric Modeling PPT9: Global and local interpolation PPT and video are due no later than March 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

Curve and Surface Fitting Suggested content: interpolation vs. approximation constraints at various locations degree, smoothness data reduction non-uniqueness, selection global versus local methods application domains

Global Curve Interpolation Suggested content: Global curve interpolation Choose knots and parameters Solve for control points

Global Curve Interpolation Suggested content: Parametrization types uniform chord length centripetal

Global Curve Interpolation Suggested content: Knot types uniform averaging

Global Curve Interpolation: Example Suggested content: Global curve interpolation detailed example data points parameters knots system of equations

Global Curve Interpolation Suggested content: Global curve interpolation examples general data set data with collinear path

Global Curve Interpolation with end Derivatives Suggested content: Global curve interpolation with end derivatives general data set solve with derivative data

Global Curve Interpolation with end Derivatives Suggested content: Global curve interpolation with end derivatives The use of end derivatives as a design tool

Cubic Spline Curve Interpolation Suggested content: Cubic spline interpolations Knots and parameters System of equations

Curve Fitting with First Derivatives Suggested content: Global curve interpolation with first derivatives general data set solve with derivative data at each point

Curve Fitting with First Derivatives Suggested content: Global curve interpolation with first derivatives effect of derivative magnitudes examples

Global Surface Interpolation Suggested content: Global surface interpolation parameters in each direction the choice of knots

Global Surface Interpolation Suggested content: Global surface interpolation interpolate in one direction

Global Surface Interpolation Suggested content: Global surface interpolation interpolate in another direction

Global Surface Interpolation Suggested content: Global surface interpolation examples

Global Surface Interpolation Suggested content: Global surface interpolation examples co-planar data points

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation Choice of tangents at each point Bessel method Akima method

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation Geometric and parametric continuity

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation Parametrization differences

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation The choice of end tangents

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation Results with Bessel and Akima tangents

Local Parabolic Curve Fitting Suggested content: Local parabolic curve interpolation Interpolating corners and simple shapes

Rational Quadratic Curve Fitting Suggested content: Local rational quadratic curve interpolation The choice of middle weight

Rational Quadratic Curve Fitting Suggested content: Local rational quadratic curve interpolation Interpolation with lines and circles

Local Cubic Curve Fitting Suggested content: Local cubic curve interpolation The choice of end derivatives

Local Cubic Curve Fitting Suggested content: Local cubic curve interpolation Knots and control points

Local Cubic Curve Fitting Suggested content: Local cubic curve interpolation Examples

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation The choice of knots Computation of boundary control points Computation of the four inner control points

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation From data points to Bezier control net

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation From Bezier control net to B-spline

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation Example

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation Example

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation Handling of local features

Local Bicubic Surface Fitting Suggested content: Local bicubic surface interpolation The inability to handle irregular data points

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 interpolation Design common surfaces from points