CS 285: SOLID MODELING

Lecture #3 -- Wednesday, Sept. 7, 2011

 Warm-up:  Geometric continuity versus Parametric continuity:

1.)  Draw a curve that has G1 continuity (but not more),  but does not have C1 continuity.

2.)  Draw a curve that has C2 continuity,  but does not have G1 continuity.

A Quick Refresher on Splines

A primary concern is with the degrees of smoothness of these curves:
-- Parametric Continuity:  differentiability of the parametric representation (C0, C1, C2, ...)
-- Geometric Continuity:  smoothness of the resulting displayed shape (G0=C0, G1=tangent-cont., G2=curvature-cont. )

Cubic Bezier Curves

Properties of Bezier Curves

Construction of Bezier Curves

Cubic B-Spline Curves

In a nutshell, one segment depending on the 4 control points A,B,C,D, is given by the polynomial:

Q = A(1 -3t +3t² -t³)/6 + B(4 -6t² +3t³)/6 + C(1 +3t +3t² -3t³)/6 + D(t³)/6

thus the point at t=0 is given by  A/6 + 4B/6 + C/6,  and the point at t=1 is given by  B/6 + 4C/6 + D/6.
 
Assuming for the moment a closed curve with N=6 control points,
such a curve would be described as a sequence of N=6 cubic curve segments,
each one of which is controlled by four consecutive control points,
(but producing a curve segment that is only about as long as the distance between the two middle control points.)
Because a subsequent curve segment reuses three of the control points of the previous segment,
they blend together in a very smooth (C2-continuous) way.

Properties of Cubic B-Splines

The Design/Modeling/Prototyping Process

1. The Creative Spark  (--> a personal mental image)
   Where do you get your best ideas?
   What can you do to enhance the creative flow?
   Shockley's model of the "creativity pump" in the brain.
2. Initial Sketch or Mock-up  (--> something that others can see)
   How do you visualize, realize your ideas?
   What materials may be useful to make conceptual models?
3. Transformation into a CAD model  (--> something a computer can read)
   How do you get those ideas into the computer?
   ==> Focus of your homework assignment.
4. Implementation Concerns  (--> something a computer can "understand")
   What do you need to do to turn that data into a solid model?
5. Design Refinement  (--> something that can be physically realized)
   Enter the concerns about fabrication. --> Design for manufacturing.
   
6. Rapid Prototyping  ( something that can be built on a RP machine)
   What are the possibilities? Overview over various RP methods and processes (more later).

Introductions / Presentations of Assignment #1 / Discussions

Pax Mundi (fabrication process)   -- Perhaps next time ...

Wrap-up on Space Curves and Sweeps  (look at notes in Lecture #2)

• see sweep description
• show SweepDemo1 (and others...)
  

Procedural, Parameterized Modeling with SLIDE

Introduction to SLIDE

• SLIDE originated as a toy rendering system for CS 184
• SLIDE lies between Mathematica / Matlab and traditional CAD tools (Solidworks, Autocad)
• It describes boundary representations (B-reps)
• Most numerical values can be substituted by expressions that are evaluated in each rendered frame.
• It offers interactive fine tuning of critical parameters via sliders
• It builds on OpenGl (for rendering) and Tcl (user interface, expression parsing)
• Main drawbacks:
• Not a properly maintained system.
• Tcl is a pain during the debugging process!
  

Some SLIDE and Tcl Basics

Install SLIDE on your own computer:

To help with creating your own environment: 
Here's a link to the sweep framework (with gui) that we used in CS 184 last semester.
It should work on windows, mac and linux (tested on the hive cluster in soda 330).

http://eecs.berkeley.edu/~jima/sweep_skeletoncode_aug2011.zip

Homework Assignment (9/7 to 9/14):

A#2: Using SLIDE to create interactive Venn diagrams