CS 285: SOLID MODELING

Lecture #7 -- Tue, Sep. 18, 2007.

Warm-up Thinking Exercise:

 How do you get a sweep along a (crooked) closed curve to close "gracefully" on itself ? 

Some Basic Concepts Behind the Sweep Implementation in SLIDE

• Finding the Tangent
• Normal Plane
• Osculating Plane
• Normal vector
• Binormal
• Difference between Normal and second derivative
• The three coordinate planes and their relations to the 3 vectors.

• How to properly join cylidrical tubes at an angle.
• How to join prismatic tubes, so edges line up.
• "Azimuth" and "axturn".
• How to calculate the torsion minimizing azimuths.
• The "twist" parameters.

• How to gracefully join the two ends so that prism edges line up
• How well does SLIDE do this ?  Test cases: Hamiltnian cycles on cube, dodeca, face-diagonals of dodeca, ...
  

• Any smooth curve in computer graphics becomes piecewise linear at some point.

•  see sweep description
• explore these parameters in the new homework assignment, study monogram.slf and monomesh.slf

Visualization of Symmetry Groups Using Shape Generator Programs

Understanding Chart I:  with "Sculpture Generator I"  {The program for you to experiment with}

Understanding Chart II:  with "Escher Sphere Editor"  {The program for you to experiment with}

From a Graphical Design to a Realizable 3D Solid Part

• Need to distill out an individual tile;
• Need to give the tile some thickness,
• and possibly some relief in the form of a height field;
• Need to provide a (possibly simpler) back-surface;
• Need to connect these two surfaces into a coherent B-rep with side walls;
• Also may have to figure out a coloring pattern for the various tiles.

Representations for Solid Modeling

• What is easiest way for the designer to describe the part:
  -- instancing, boolean operations, maintain symmetry, allow controlled space warps, ...
  
• What is the best way to visualize the result of a designer's input:
  -- interactive speed, resolve booleans to screen resolution, rendering enhancements: shadows, depth queues ...
  
• How can a possible design most easily be analyzed for consistency, volume, weight distribution, srength, ...:
  -- need to deal with volumetric information explicitly: tetrahedralization, finite-element meshing, voxelization, ...
  
• How can the finished design best be transmitted to someone else:
  -- description needs to be unambiguous, precise, efficient, easy to parse and process, ...  (unlike .STL).
  
• What is the best representation for the manufacturing process:
  --  primitives relevant to the manufacturing process -- strongly depends on type of process:
• Layered manufacturing:  Collection of 2D contours or raster maps corresponding to each slice level.
• Machining on a milling machine:  Starting shape plus a collection of features (pockets, drill holes) that need to be removed.
  

Current Homework Assignment#4: (Due 9/20/07:  08 am, electronically)

Use the sweep facility in SLIDE to generate your monogram.