PPT11: Advanced Surface Construction Techniques CAP 6736 Geometric Modeling PPT11: Advanced Surface Construction Techniques PPT and video are due no later than April 5 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

Swung Surfaces Suggested content: swung surfaces profile and trajectory curves surface construction

Swung Surfaces Suggested content: swung surfaces surface examples

Skinned Surfaces Suggested content: skinned surfaces cross-sectional curve examples

Skinned Surfaces Suggested content: skinned surfaces making curves compatible common knot vector

Skinned Surfaces Suggested content: skinned surfaces surface construction via interpolation

Skinned Surfaces Suggested content: skinned surfaces parameters and knots

Skinned Surfaces Suggested content: skinned surfaces skinning using a guide curve

Skinned Surfaces Suggested content: skinned surfaces skinning using a guide curve and derivatives

Skinned Surfaces Suggested content: skinned surfaces with spine curve examples

Skinned Surfaces Suggested content: skinned surfaces with spine curve examples

Skinned Surfaces Suggested content: skinned surfaces with spine curve section curve positioning

Skinned Surfaces Suggested content: skinned surface issues rational cross-sectional curves give rise to negative weights

Skinned Surface Revisited Suggested content: skinned surface skinning in practice

Skinned Surface Revisited Causes of lofting problems: Parametrization inconsistencies: parameters must flow the same way along each section curve Positioning inconsistencies: section curves must be placed with care or wiggles or even self intersections may occur Continuity inconsistencies: rational curves must be parametric continuous in homogeneous space not just in Euclidean space Weight problems: large weight changes may cause negative weights during interpolation and weight scaling may produce nonsensical surfaces

Skinned Surface Revisited Suggested content: skinned surface skinning to approximate cross-sectional curves Remove bad parametrization and weight problems

Skinned Surface Revisited Suggested content: skinned surface examples

Skinned Surface Revisited Suggested content: skinned surface examples

Swept Surfaces Suggested content: swept surfaces trajectory and section curves translational sweep

Swept Surfaces Suggested content: swept surfaces example

Swept Surfaces Suggested content: swept surfaces trajectory and section curves non-translational sweep surface construction

Swept Surfaces Suggested content: swept surfaces no trajectory control

Swept Surfaces Suggested content: swept surfaces no scaling scaling of section curves

Swept Surfaces Suggested content: swept surfaces no trajectory control

Swept Surfaces Suggested content: swept surface problems self intersection wavy surfaces

Swept Surfaces Suggested content: swept surface problems incorrect curve placement causes flipped surfaces

Swept Surfaces Suggested content: swept surface problems better curve placement with a local moving frame

Gordon Surfaces Suggested content: Gordon surfaces bi-directional curve network compatibility conditions blending functions construction of Gordon surface

Gordon Surfaces Suggested content: Gordon surfaces construction of Gordon surface u-directional lofting

Gordon Surfaces Suggested content: Gordon surfaces construction of Gordon surface v-directional lofting

Gordon Surfaces Suggested content: Gordon surfaces construction of Gordon surface interpolation through intersection points

Gordon Surfaces Suggested content: Gordon surfaces construction of Gordon surface from three surfaces

Coons Surfaces Suggested content: Coons surfaces bi-linearly blended patch to four boundaries

Coons Surfaces Suggested content: Coons surface construction ruled surfaces in both directions

Coons Surfaces Suggested content: Coons surface construction bi-linear surface and Coons patch

Coons Surfaces Suggested content: bi-cubically blended Coons surface boundary curves, cross-derivatives and twist vectors surface control points

Coons Surfaces Suggested content: bi-cubically blended Coons surface cubic blend in one direction

Coons Surfaces Suggested content: bi-cubically blended Coons surface cubic blend in another direction

Coons Surfaces Suggested content: bi-cubically blended Coons surface bicubic tensor product surface

Coons Surfaces Suggested content: bi-cubically blended Coons surface

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 advanced surface construction