19-surfaces-parametric-implicit

# 19-surfaces-parametric-implicit - Reading for last week and...

This preview shows pages 1–4. Sign up to view the full content.

1 Curves and Surfaces Lecture 19 CPSC 578/478 Spring 2005 Curves: Hermite, Catmull-Rom, Bezier, B-Spline, NURB Surfaces from splines: Revolution, Lofted, Tensor Product Implicit Surfaces Reading for last week and this week: Text, Chapter 13 Supplement with http://graphics.idav.ucdavis.edu/graphics/CAGDNotes/homepage.html And http://www.siggraph.org/education/materials/ HyperGraph/modeling/splines/splines0.htm Class Calendar: April 4: assignment # 3 due April 6: assignment #4 topic/teams due April 11: assignment #4 short proposal due April 13: Quiz #2 April 18: assignment #4 long proposal due April 20: assignment #4 5 min oral proposal/preliminary results May 10: assignment #4 code, executable report due Assignment #3: Check materials section for help sent in by people in class, Jianye. Currently grinberg_modeler_spring2005_ linux.zip Course Syllabus I. Image processing II. Rendering III. Modeling IV. Animation V. Advanced Topics Image Processing Modeling Animation Rendering

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Modeling How do we ... Create 3D objects? Store 3D objects? Use 3D objects? Different methods for different object representations In different phases (creation, storage, use) the same object may be represented in different ways. 3D Object Representations Raw data Point cloud Range image Polygon soup Surfaces Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Skeleton Application specific Conics: useful shapes inconvenient in 3D Polynomial Functions: hard to control Splines Linear: not smooth parameterization basis functions knots Hermite: global, not always predictable cubic basis functions composite parameterization Catmull-Rom: fast for animation, less smooth, Bezier: predictability, but no local control convex hull property B-Splines: no conics, no perspective transform NURBs!! Last time Correction from last time: Except for the tangent, Frenet Frame undefined for straight line A Physical Spline Instead use a series of segments defined in parametric form. u ) ( ) ( ) ( u z z u y y u x x = = = These functions determined by coordinates of P n
3 (Exaample for Hermite basis functions) u u 2 u 3 P(u)=(x(u),y(u),z(u)) Matrix representation Basis functions over one segment Bezier Curves and B-Splines: Convex Hull Property 1 ) ( ) ( ) ( 4 .. 1 4 .. 1 = = = = u B u B x u x i i i i i Bezier Curves: Convex Hull Property Passes through end points Continuity not guaranteed Iterative evaluation: de Casteljau algorithm B-Splines: Convex Hull Property Does not pass through points Continuity guaranteed (Iterative evaluation also exists) Bspline One segment Bspline

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern