PPT8: Common Surfaces as NURBS CAP 6736 Geometric Modeling PPT8: Common Surfaces as NURBS PPT and video are due no later than March 8 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

Bilinear Surfaces Suggested content: Bilinear surfaces: control points and knots Planar as well as non-planar surfaces Example: saddle design

General Cylinder Suggested content: General cylinder as a sweep Profile curve + sweeping

General Cylinder Suggested content: General cylinder examples closed cylinder open cylinder general sweep

Ruled Surfaces Suggested content: Ruled surfaces rail curves ruling surface form control points and knots

Ruled Surfaces Suggested content: Ruled surface examples rail curve compatibility knot merging surface form several examples

Ruled Surfaces Suggested content: Ruled surface examples rail curve after compatibility ruled surface

Ruled Surfaces Suggested content: Ruled surface examples open and closed cones conoids artistic applications

Ruled Surfaces Suggested content: Ruled surface examples the art of ruling sculptured surfaces as ruled surfaces

Ruled Surface via Symbolic Operators Suggested content: Ruled surface with symbolic operators Rational curves ruled in homogeneous space Creases in parametrization

Ruled Surface via Symbolic Operators Suggested content: Ruled surface with symbolic operators Rational curves ruled in Euclidean space

Surface of Revolution Suggested content: Surfaces of revolution Profile curve and revolution axis Requirement of revolution

Surface of Revolution Suggested content: Construction of surfaces of revolution Revolution circle knots and weights Surface control points Surface weights

Surface of Revolution Suggested content: Surfaces of revolution example Control net and surface

Surface of Revolution Suggested content: Surfaces of revolution examples Sphere and torus

Surface of Revolution Suggested content: Surfaces of revolution examples Open surfaces

Surface of Revolution in Practice Suggested content: Surfaces of revolution in practice Discrete data – profile curve – surface of revolution

Surface of Revolution in Practice Suggested content: Surfaces of revolution in practice Circle of revolution with different degrees

Non-uniform Scaling of Surfaces Suggested content: Scaling of surfaces Circle of revolution with different degrees Scaling factors and center of scaling New control points Example: ellipsoid from sphere

Non-uniform Scaling of Surfaces Suggested content: Scaling of surfaces Example: elliptic paraboloid

Three-sided Spherical Surfaces Suggested content: Corner surface problem Three-sided patch as NURBS surface

Three-sided Spherical Surfaces Suggested content: Stereographic projection to parametrize the sphere Mapping planar points onto the sphere

Three-sided Spherical Surfaces Suggested content: Creating circular boundaries for three sided patch Convert to Bezier form

Three-sided Spherical Surfaces Suggested content: Three sided patch as degenerate Bezier surface Control points and 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: Design common surfaces using NURBS Design composite surfaces