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24-786  GEOMETRIC MODELING  Spring 2002

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Please check this page regularly because the coverage and the schedule are subject to change based on students' needs.   Download handout files, print them, and bring them to class. 

#

Date

Topics

Reading
Assignments

Handouts

Problem
Sets

1

1/14

Course Outline
Mechanical CAD/CAE

1. BASIC GEOMETRY
  
   1.1 Vectors and Matrices 

class home page
pp.1-18 (intro)
pp.431-437 (vector)
pp.431-437 (matrix)

calendar.pdf
MCAD industry
MCAE industry
Sketchpad

PS1 Out 

2

1/16

   1.2 Lines and Planes


Review  programming

 

 

 

1/21

   Martin Luther King Day
   (no afternoon classes)

 

 

   

3

1/23

   1.3 Transformations

pp.439-471 

vrml-sample.pdf
vrml-sample.wrl
transform-chain.pdf
transform-chain.wrl
vrml97_specs.zip
vrml_examples.zip
robot-parts.wrl

PS1 Due
PS2 Out  
   

4

1/28

   (PS1 feedback)
   1.3 ...
   (VRML2 tutorial)

 

general rotation matrix

 

5

1/30

   1.3 ...

  triceratop.dat
triceratop1.jpg
triceratop2.jpg

PS2 Due
PS3 Out 

6

2/4

   1.4 Areas and Volumes
  (C macros for vectors and rotations)

 

 

7

2/6

 

  

 

PS3 Due

PS4 Out

8

2/11

QUIZ 1: Introduction

 

  

 

9

2/13

2. SOLID MODELING
   2.1 Introduction
   2.2 Mathematical Model of Solids
     2.2.1 Mathematical Object
     2.2.2 Point-Set Models
  (ST1: Wiereframe to Solid Conversion)

pp.281-373


PS4 Due
PS5 Out
  

10

2/18

  (Quiz1 feedback)
     2.2.3 Boundary Based Models
  (PS4 Preview)

 

graded Quiz1
plane model examples

 

11

2/20

     2.2.3 ...

 

  

PS5 Due
PS6 Out

12

2/25

  2.3 Constructive Solid Geometry
  2.4 Decomposition Models
     2.4.1 Spatial Occupancy Enumeration
     2.4.2 Octrees

pp.318-356

tree traversal

   

13

2/27

     2.4.3 kD Tree
     2.4.4 BSP Tree

pp.367-372

 

PS6 Due
PS7 Out  

14

3/4

  2.5 Boundary Representation
     2.5.1 Data Structure
     2.5.2 Euler Operators
     2.5.3 Modeling Operations

 

regularized Boolean set op
half-edge data structure
Euler operator worksheet

   

15

3/6

  2.6 Advanced Issues in Solid Modeling
     2.6.1 Non-Manifold Geometry
     2.6.2 Bounding Geometry for Collision Detection
     2.6.3 Mesh Generation

 pp.19-38

 

PS7 Due
PS8 Out 

16

3/11

QUIZ 2: Solid Modeling

 

 

 

17

3/13

3. CURVES AND SURFACES
  3.1 Basic Curves
     3.1.1 Explicit, Implicit, and Parametric Forms
     3.1.2 Algebraic & Geometric Forms
     3.1.3 Analytic Curves in 3D
  (Solid Modeling Review)

 

 

PS8 Due
PS9 Out

18

3/18

  3.2 Hermite Curves
     3.2.1 Algebraic & Geometric Forms
     3.2.2 Matrix Forms
     3.2.3 Tangent Vectors and Controllability
     3.2.4 Four Point Interpolation
     3.2.5 Continuity

pp.39-80

  

    

19

3/20

  3.3 Bezier Curves
     3.3.1 Hermite-Bezier Conversion
     3.3.2 Bezier Basic Functions
     3.3.3 Properties of Bezier Curves
     3.3.4 The de Casteljau Algorighm
     3.3.5 Composite Bezier Curves

pp.81-112

  

PS9 Due
PS10 Out

20

3/25

  3.4 B-Spline Curves
     3.4.1 Introduction
     3.4.2 B-Spline Basis Function

pp.113-142

 

 

21

3/27

     3.4.3 Multiplicity and Continuity
     3.4.4 Bezier vs B-Splines
     3.4.5 Open B-Spline Curves

 

  

PS10 Due
Project Proposal Due
PS11 Out

 

4/1
4/3

!!  S P R I N G  B R E A K  !!

 

 

 

22

4/8

  3.5 Hermite Surfaces
     3.5.1 Algebraic & Geometric Forms
     3.5.2 Geometry Vectors

pp.169-216

 

   

23

4/10

  3.6 Bezier Surfaces
     3.6.1 Geometry Vectors
     3.6.2 Converting Hermite to Bezier
     3.6.3 Composite Bezier Surfaces

pp.217-226

 

PS11 Due

24

4/15

4. Applications and Advanced Topics  

 

   

25

4/17

 

 

  

  

26

4/22

Project Presentations

 

 

Project Report Due

27

4/24

Project Presentations

 

  

 

28

4/29

 Course summary

 

 

 

29

5/1

QUIZ 3: Curves and Surfaces

 

  

 

 

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Send mail to shimada@cmu.edu with questions or comments about this web site. 
(c) Kenji Shimada, Carnegie Mellon University, 2000