• Ahmedabad-Visual Design Office

• Kolhapur-Mechanical Design Office

• Saki Naka – Die Manufacturer

• Lucknow- Soap manufacturer

A Solid Modeling Fable

Ahmedabad-Visual Design

• Input: A dream soap tablet

• Output:• Sketches/Drawings• Weights• Packaging needs

Soaps

More Soaps

Ahmedabad (Contd.)

Top View

Front View Side View

Kolhapur-ME Design Office

• Called an expert CARPENTER

• Produce a model (check volume etc.)

• Sample the model

and produce a data-

set

Kolhapur(contd.)

Kolhapur (contd.)

• Connect these sample-points into a faceting

• Do mechanical analysis

• Send to Saki Naka

Saki Naka-Die Manufacturer

• Take the input faceted solid.

• Produce Tool Paths • Produce Die

Lucknow-Soaps

• Use the die to manufacture soaps

• Package and transport to points of sale

Problems began…

• The die degraded in Lucknow

• The Carpenter died in Kolhapur

• Saki Naka upgraded its CNC machine

• The wooden model eroded

But

The Drawings were there!

So Then….

• The same process was repeated but…

The shape was different!

The customer was suspicious and sales dropped!!!

The Soap Alive !

What was lacking was…A Reproducible Solid-

Model.• Surfaces defn• Tactile/point

sampling• Volume

computation• Analysis

The Solid-Modeller

Modeller

OperationsRepresentations

The mechanical solid-modeller

Operations• Volume

Unions/Intersections• Extrude holes/bosses• Ribs, fillets, blends

etc.

Representation• Faceted Solid• Cloud of Points• STEPP• Boundary-Rep (b-rep)• .sldprt

Examples of Solid Models

Torus Lock

Even more examples

Slanted Torus Bearing

Examples (Contd.)

Solid Model of an Ice-Cream Machine

Sample Representations

Other Modellers-Surface Modelling

Chemical Plants

• Design Rules

-process rules

-tolerances• Civil-Mechanical

Co-Design

-facility design

-accessibility

-safety

Chemical plants (contd.)

Chemical Plants (contd.)

Advanced Surface Modelling

Human Cortex

Manual Surface Sampling,/ model consists of 24,000 planer facets

Advanced Surface Modelling (Contd.)

The above surface model was created by using the

software tool (Nuages) by Bernard Geiger

Voxel based re-construction shows the surface decimated to about 22500 vertices and 45000 triangles

Our Course-Theory

• Topology-combinatorial entities and their relationships

• Geometry- parametrizable entities and their representations

• Operations- some of them and their implementations

source:www.cse.iitb.ac.in/~sohoni CAGD course notes

Our Course-Applications

• Basic solid-modelling

• Design Trees and re-parametrization

• MIL (B-rep) and geometry

Course Schedule

Time AM AM PM PM

Day 1 SM-Fable.ppt SM-Primer.ppt

SM-Practical

Tutorial

3d

Day 2 SMInternals.ppt

Geometric-Topology

Polynomials.pdf

Tutorialpolynomials

Day 3 Curves.pdf Surface.pdf Application I

TutorialCurves and Surfaces

Day 4 Spline.pdf Operation.pdf

Application II

TutorialOpns/Cons.

Day 5 Construction.pdf

Wrap-Up ApplicationIII

TEST

Contents I

SM-Fable Motivate SM, examples SM and structure of SM

SM-Primer Practical introduction to an SM

SM-Internals Kernel/Husk dichotomy. Entities-face/edge/co-edge.

Topology and applications

Geometry-Topology

The two-tier representation. Parametric vs. Implicit. Sample parametrizations, trim curves

Polynomials Polynomials and the approximation problem, lagrange interpolation, and the bernstein base

Curves The construction of Bezier-Bernstein curves, control polygons, end calculations, elevation

Surfaces The 2d analogue of bernstein. Tensor-product surfaces, end conditions

Contents II

Splines The piece-wise polynomial paradigm, knot insertion and evaluation

Operations TheNewton/Raphson Solver, the projection problem, intersections

Constructions The constructor, intersection curves, extrudes, blends