C omputer G raphics, TU Braunschweig S. Havemann, GML1 Generative Mesh Modeling Sven Havemann Dieter...

S. Havemann, GML 1Computer Graphics, TU Braunschweig

Generative Mesh Modeling

Sven Havemann Dieter W. Fellner

Institut für ComputerGraphik

TU Braunschweig, Germany


The “State of the Art”


A Provocative Statement Great achievements in Computer Graphics…

Appearance: From Solid Textures to Pixel Shaders Shape Processing: Simplification to Wavelets Global Illumination

… but now let’s turn our attention to the people at the end of the food chain: Those who are doing the actual 3D modeling

Without models, there’s nothing to display! Hypothesis:

Lack of easily available 3D model creation facilities greatest obstacle to spread of 3D technology today


Modeling Problem: “Learn Maya” People (in industry) want to sell goods and services –

not have their own modeling department Roof tiles: ~75 kEuro modeling costs (personal

communication)

… and what do you do with those models? Creation of 3D models should require the same level

of expertise as creation of spreadsheets! Integration into 3rd party applications

Modeling engine as plugin or dll


Issues with Simplification Increasing need for LOD: More triangles than pixels But

Simplification breaks the modeling history (preprocessing)

Simplification breaks symmetry Highest resolution is limited by input resolution


Problems with Current TechnologyA. The Modeling Bottleneck

• limited changeability and re-usability of objects• 3D modeling is to large extent a manual task

B. Model File Sizes• Simplification breaks modeling history• Highest resolution limited by input resolution

C. Digital Libraries of 3D Objects• Design variations• Problems: Consistency, versioning, shape matching

D. Virtual Worlds are too static• Basically change only transformation matrices (…)• Careful look at state of the art in computer games!


3D Modeling – An Abstract View 3D modeling is an incremental process

Interactive application of functions/tools on a shape in order to obtain another

All 3D modeling is procedural modeling! Selection of the next operation is not arbitrary,

but based on a plan in the artist’s mind Often next step depends on outcome of previous step

3D modeling is what other people call programming! Striking similarity: Conditional decisions, loops, etc. Today's artists are in fact programming a shape,

probably without noticing that, and with not much support for it from their system


3D Modeling – Abstract SolutionA. Computers are fast (500M mul/s) – and they get faster B. 3D Modelers already provide interactive toolsC. Description of modeling process more compact than

description of modeling result

Consequence:Generate geometric primitives only on demand

Look for a different shape representation “smallest common denominator” for the

description of procedural shapes It must be a full programming language! Problem: Artists shall not do literal programming


Generative Mesh Modeling

Our proposal for a solution that might alleviate some of these problems


The shape description problem Shape acquisition vs. interactive modeling

Highly regular shapes with slight variations Shapes with self-occlusion

Fundamental question:“What is the right way to describe the construction of a shape or a shape class?”

Different aspects: What are the “essential” degrees of freedom

of a given shape construction? What low-level shape representation? What operations on this representation? How can shape construction be formalized?


Our Approach: Modeling Engine Low-level shape representation:

Polygonal solids + freeform surfaces Hybrid hierarchical architecture

Catmull/Clark surfaces

BRep meshes

Euler operators

GML


Bottom Layer: Catmull/Clark After first tesselation: only quads

1 patch per quad Face degree n n patches Quad 3 times subdivided: 9 9 vertices/patch Only 2 possibly irregular points per patch

Adaptive refinement: pre-computed triangle strips

[ Havemann, Visual Computer 2002 ]


Irregular Vertices: Vertex & Face Rings

Tesselation hierarchy: 22, 33, 55, 99 Down-sampling for free 75400 Patches = 7.4 M / sec on P4 1700 MHz

Tesselation on the fly


Second Layer: Combined BReps

Unified data structure for shapes with both

polygonal and free-form parts


red: sharp edgegreen: smooth edge

1. Vertex classification No. of incident sharp edges

< 2 smooth or dart = 2 crease > 2 corner

2. Face classification smooth edge? smooth Only corners? polygonal Otherwise: sharp

Edge Sharpness


Sharp Faces & Rings Sharp face: BSpline border curve Rings: Trimming of polygonal or sharp faces


Combined BReps - Performance View-cone culling:

sphere/cone intersection Backface culling:

normal cone per face

Animation on P4 1700 MHz /Geforce 4

16K vertices59K halfedges13K faces54K patches 7M triangles


Third Layer: Euler Operators and

Progressive Combined BReps

Mesh manipulationwith incrementaltesselation update


Euler operators Mesh access exclusively

through halfedges Halfedges always come

in pairs (no border) Topologic consistency vs.

Geometric consistency

i. Each Euler operator maintains topologic consistency

ii. Every 2-manifold mesh of any genus can be built

Closed and sufficient set of mesh construction operators


1. Make vertex edge face shell

Shell: connected component Creates degree 2 face (2 vertices, 2 halfedges)

No face normal – but topologically correct

V-E+F = 2(S-H)+R 2-1+1 = 2(1- 0)+0

Extended Euler-Poincaré:


2a. Make edge vertex

Creates dangling vertex Good for conversion polygon face

V-E+F = 2(S-H)+R 1-1+0 = 2(0- 0)+0


2b. Make edge vertex

makeEV: e0,e1 incident to same vertex Also known as vertex split

V-E+F = 2(S-H)+R 1-1+0 = 2(0- 0)+0


3. Make edge face

makeEF: e0,e1 must be incident to same face Order determines orientation

V-E+F = 2(S-H)+R 0-1+1 = 2(0- 0)+0


4. Make edge kill ring

Rings: trim polygons in face interior Rings are cw oriented

V-E+F = 2(S-H)+R0 -1+0 = 2(0- 0)-1


V-E+F = 2(S-H)+R0 -0+1 = 2(0+1) -1

5. Make face kill ring hole(or make face shell kill ring)

V-E+F = 2(S-H)+R0 -0+1 = 2(1- 0) -1

Ring Backside of two-sided quad


6./7. Geometric operators

Both are self inverse Don’t affect topology

moveV change vertex positionsharpE change edge sharpness


Log each Euler operator operator sequence Like split sequence from progressive triangle mesh But may also contain destructive operators!

Dependencies between operators: DAG But: Inconsistent intermediate meshes Euler macros: grouping of sub-sequences Dependency DAG on Euler macro level Useful for selective undo/redo, Useful for macro culling using active tree

[ Luebke/Eriksson, Siggraph 97 ]

Euler Macros


Log each Euler operator operator sequence Like split sequence from progressive triangle mesh May also contain destructive operators

Edge collapse: killEF, killEF, killEV, moveV

Euler Macros


C++ API: obvious & simpleEdge* makeVEFS (const Vec3f& p0, const Vec3f& p1, bool sharp);bool killVEFS (Edge* e);Edge* makeEV (Edge* e0, Edge* e1, bool sharp, const Vec3f& p);bool killEV (Edge* e);Edge* makeEF (Edge* e0, Edge* e1, bool sharp);bool killEF (Edge* e);Edge* makeEkillR (Edge* eRing, Edge* eFace, bool sh);Edge* killEmakeR (Edge* e);bool makeFkillRH (Edge* eRing);bool killFmakeRH (Edge* eRing, Edge* eBase);bool moveV (Edge* e, const Vec3f& pNew);bool sharpE (Edge* e, bool sharp);

bool moveR (Edge* eRing, Edge* eDest);bool materialF (Edge* e, int matid);


Top Layer: The GML

Proposal for a “smallest common denominator”

for the description of procedural shapes


Tokens are pushed on a stack (old pocket calculator)

Operators pop items from the stack, process them, and push the result

Programs are just arrays of tokens Program execution is execution of each token

Stack Based Language: Principle

2 3 add 4 mul2 3 add 4 mul 22 3 add 4 mul 32

2 3 add 4 mul 52 3 add 4 mul 45

2 3 add 4 mul 20

Program

Stack


GUI Automation Problem with great tools: You must use them Basic idea for automatization:

Put a language behind the GUI

The dialog box turns into

Ideally, this language backend is invisible

10.00 2.80 0.25 5 2 1 createCube

Screenshot from 3DStudio Max


Automation of Dialog Boxes Different sets of parameters are possible:

Parameter sets can be computed (spreadsheet)

10.00 2.80 0.25 5 2 1 createCube

{ 10.00 2.80 0.25 5 2 1 } /wall def{ 10.00 0.10 0.10 8 1 1 } /rod def{ 1.00 1.00 1.00 2 2 2 } /unitcube defwall createBoxrod createBox

{ dup dup 1 1 1 } /cube def4.82 cube createBox

New menu items


All Functionality from Operators Example:

Stable extrude, avoiding self-intersections


All Functionality from Operators Example:

Stable extrude, avoiding self-intersections


C++ API for GML operatorsclass GMLOpCross : public GMLOp{public: GMLOpPrelude(Cross,cross) GMLOpComment(" u:P3 v:P3 -> w:P3 %n returns the cross product of u and v, so w is perpendicular to both u and v.")

virtual bool apply (GMLInterpreter& inter) { Var* v1 = inter.pop_stack(); Var* v0 = inter.pop_stack_leave(); if(inter.error() || !v0isP3() || !v1isP3()) { return inter.setError(GMLInterpreter::TypeError); } v0->set( v0asP3().cross(v1asP3()) ); inter.commit_pop(); return true; }};

wrapped library function


Modeling Engine The GML is a library on top of OpenGL Designed as plugin modeler

– or modeling plugin Extensible etc.


Current State Four-layer architecture works reasonably stable

and with reasonable performance The core engine for modeling is available

PhD

~290 operators in 10 libraries today core, math, vector, geometry, brep, modeling, …

Tutorial just finished, first students work with it http://graphics.tu-bs.de/gml


GML: Interactive 3D Modeling Spreadsheet modeler: Code generation in background

Create new tools out of existing ones Re-use existing solutions to modeling problems Automated 3D modeling Model evaluation on the fly

Direct manipulation of a multiresolution mesh Model representation: Combined BRep Both polygonal and subdivision surface models using

smooth and sharp edges Undo/redo using Euler operations Built-in adaptive Level-of-Detail (frame to frame!)


Next steps “Spreadsheet Modeler” Experiments with input devices:

Video tracking, CAVE 3D GUI is needed for certain plugins (ActiveX) modeling tools in digital library, web access Future developer hierarchy

C++ level: create new GML operators (.dll) GML level: domain-specific modeling tools (.genmod) Spreadsheet level: Glue tools together, forming new tools Pure users (code completely hidden)


Summary & Discussion GML code generation in background

Think of Postscript printer driver Modeling: Create new tools out of existing ones,

re-use existing solutions to modeling problems Style libraries: GML is a functional language! Automated 3D modeling Semantic level of detail

Store tools used, not model created More space efficient

Model evaluation on the fly


Summary Procedural Modeling uses high-level tools for

(interactive) model manipulation Idea: Store tools used, not model created

More space efficient Computers are fast: Evaluate model description

only on demand – at viewer runtime! GML as low-level description format for all

kinds of procedural models – really?


More fundamental issues

Different ways to think about shape?


Theoretical Aspects: Shape Complexity Kolmogorov complexity:

“Given a bit sequence and a computer model, what is the size of the smallest computer program to produce that sequence?”

Depends on the set of available basic operations Intrinsic Shape Parameters:

Explicitly depend on other parameters, are computed Extrinsic Shape Parameters: Degrees of freedom Conversion: In both directions?

We propose as shape complexity measure: The number of GML tokens for a shape / shape class


Quest for the “Nature of Shape” Investigate existing real-world construction systems

to determine their modeling vocabulary: Lego Fischer-Technik Metal construction kits (z.B. Märklin) Ikea Architecture, Mechanical Engineering…

Which are the domain dependent modeling operations? Is it possible to find underlying set of general shape

construction operations? Now formally in GML terms:

“Find minimal but sufficient set of builtin operators”

Date post:	23-Dec-2015
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C omputer G raphics, TU Braunschweig S. Havemann, GML1 Generative Mesh Modeling Sven Havemann Dieter...

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