Computational DesignForward and Inverse Methods

1

Computational Design

Design: decide upon the look and functioning of an artifact (a building, garment, toy, etc), typically by making a detailed blueprint or drawing

Computational: related to computers and mathematical calculations

Basic ingredients for computational design:• Mathematical model that predicts behavior of a system

• A set of parameters that affect the system’s behavior

2

Computational Design

Forward design: direct manipulation of design parameters• Level of abstraction is key

• Exploration of design spaces through suggestions

Inverse design: automatically infer design parameters from functional specifications• Optimization-based

It is often a good idea to mix and match elements of forward and inverse design

Forward Design

Editing 3D Models as a simple example

Editing 3D Models

Options:

• Directly edit mesh vertices Finding the right level of abstraction is key!

Editing 3D Models

Options:

• Directly edit mesh vertices Finding the right level of abstraction is key!

• Cage-based editing

Cage-based mesh editing

Embed 3D model in a coarse mesh (cage)

Edit cage vertices, deform model with it automatically

Barycentric coordinates

Ratio of areas (volumes in 3D)

Conceptually the same

in higher dimensions

Cage-based mesh editing

can’t precisely control surface properties

Editing 3D Models

Options:

• Directly edit mesh vertices Finding the right level of abstraction is key!

• Cage-based editing

• Skeletal Rigs

Skeletal Rigs

Skeletal Rigs

Skeletal Rigs

Editing 3D Models

Options:

• Directly edit mesh vertices Finding the right level of abstraction is key!

• Cage-based editing

• Skeletal Rigs

• Physics-based methods for mesh editing

Surface vs volumetric models

Editing 3D Models

Options:

• Directly edit mesh vertices Finding the right level of abstraction is key!

• Cage-based editing

• Skeletal Rigs

• Physics-based methods for mesh editing

Simulation as predictive tool for

forward design

18

Forward Design

Finding the right level of abstraction is key

• Navigating parameter spaces Intuitive UIs

Restrict design space to some extent

Trade-off between flexibility and ease of use

• FAST simulation methods are ideal

Alternatives?

• Explore design space via reasonably-chosen suggestions

Design Space Exploration

J Marks et al. Design galleries: a general approach to setting parameters for

computer graphics and animation. SIGGRAPH 1997

Design Space Exploration

Sample parameter space

• Poisson sampling

Present design space in a manageable way

• Cluster similar designs

• Visualize designs exhibiting greatest variation

• Hierarchical refinement

Design Space Exploration

Eric Brochu, Tyson Brochu and Nando de Freitas. A Bayesian Interactive Optimization

Approach to Procedural Animation Design. ACM SIGGRAPH/Eurographics

Symposium on Computer Animation, 2010

Design Space Exploration

Many-Worlds Browsing for Control of Multibody Dynamics, Twigg

and James, SIGGRAPH 2007

Many Worlds Browsing…

vt

`compute and

apply impulse

vt+1

Sampling Plausible Worlds

[O’Sullivan et al., 2003]

Many Worlds Browsing…

Interactive Browsing – various criteria

Many Worlds Browsing

Computational Design

Forward design: direct manipulation of design parameters• Level of abstraction

• Exploration of design spaces through suggestions

Inverse design: automatically infer design parameters from functional specifications• Optimization-based

It is often a good idea to mix and match elements of forward and inverse design

Inverse Design

Discrete mechanical system

𝐩 = argmin 𝑑(𝐱(𝐩), 𝐱𝑡) s. t. 𝐂(𝐱(𝐩), 𝐩) = 𝟎𝐩

• State 𝐱(𝑡)• Parameters 𝐩• Simulation 𝐩 → 𝐱 𝐩, 𝑡• Constraints 𝐂(𝐱, 𝐩) = 𝟎• Objective 𝑑(𝐱, 𝐱𝑡)

Given desired states 𝐱𝑡, find

Inverse Design

State ParametersTarget Result

Simulation

Optimization

Printed Mold

Silicone Balloon

Computational Design of Rubber Balloons, Skouras et al., Computer

Graphics Forum, 2012

Computational Design

Forward design: direct manipulation of design parameters• Level of abstraction

• Exploration of design spaces through suggestions

Inverse design: automatically infer design parameters from functional specifications• Optimization-based

It is often a good idea to mix and match elements of forward and inverse design