lecture 2 3d modeling - tongji universitysse.tongji.edu.cn/jiajinyuan/acg2012fall/lecture 02-3d...

3D Modeling, Advanced Computer Graphics Shuang LIANG, SSE, Fall 2012

Lecture 23D Modeling

Dr. Shuang LIANGSchool of Software Engineering

Tongji UniversityFall 2012


Lecturer

Dr. Shuang LIANG• Assisstant professor, SSE, Tongji

– Education» B.Sc in Computer Science, Zhejiang University, 1999-2003» PhD in Computer Science, Nanjing Univerisity, 2003-2008» Visit in Utrecht University, 2007, 2008

– Research Fellowship» The Chinese University of Hong Kong, 2009» The Hong Kong Polytechnic University, 2010-2011» The City University of Hong Kong, 2012

• Contact– Office: Room 442, JiShi Building, JiaDing Campus, TongJi (Temporary)– Email: [email protected]


Outline

• What is a 3D model?• Usage of 3D models• Classic models in computer graphics• 3D model representations

• Raw data• Solids• Surfaces


What is a 3D model? 3D object using a collection of points in 3D space,

connected by various geometric entities such as triangles, lines, curved surfaces, etc. It is a collection of data (points and other information)


What is a 3D modeling? The process of developing a mathematical

representation of any three-dimensional surface of object via specialized software.


Outline




Usage of a 3D model The medical industry uses

detailed models of organs


Usage of a 3D model The movie industry uses them as characters and

objects for animated and real-life motion pictures


Usage of a 3D model The science sector uses them as highly detailed

models of chemical compounds


Usage of a 3D model The architecture industry uses them to demonstrate

proposed buildings and landscapes through Software Architectural Models


Usage of a 3D model The architecture industry uses them to demonstrate

proposed buildings and landscapes through Software Architectural Models

Microspot Interiors Professional is the award-winning 3D modeling software and interior design program for Mac. Design and envision interior home designs with the power and ease of Interiors.


Usage of a 3D model The engineering community uses them as designs of

new devices, vehicles and structures as well as a host of other uses


Outline




Classic models in CG The Utah Teapot

The "hello world" in CG A mathematical model of an ordinary teapot, which appears

solid, cylindrical and partially convex. Created in 1975 by Martin Newell, a member of the

pioneering graphics program at the University of Utah


Classic models in CG

The original, physical teapot was purchased from ZCMI (a department store in Salt Lake City, Utah) in 1974. It was donated to the Boston Computer Museum in 1984 where it was on display until 1990. It now resides in the ephemera collection at the Computer History Museum in Mountain View, California where it is catalogued as "Teapot used for Computer Graphics rendering" (http://en.wikipedia.org/wiki/Utah_teapot)

http://en.wikipedia.org/wiki/Utah_teapot


Classic models in CG The Stanford Bunny

The Stanford Bunny is a computer graphics test model developed by Greg Turk and Marc Levoy in 1994 at Stanford University.

The Bunny consists of data describing 69,451 triangles determined by 3D scanning a ceramic figurine of a rabbit.


Classic models in CG The Stanford Happy Buddha

The Stanford buddha is a computer graphics test model created with a Cyberware 3030 MS at Stanford University.

The Buddha consists of data describing 1,087,716 triangles determined by 3D scanning a real figurine.


Classic models in CG The Stanford Dragon

The Stanford Dragon is a computer graphics test model created with a Cyberware 3030 MS at Stanford University.

The Dragon consists of data describing 871,414 triangles determined by 3D scanning a real figurine.


Requirements for a 3D representation scheme Unambiguity :

When you see a representation of a solid, you will know what is being represented without any doubt.

Uniqueness : That is, there is only one way to represent a particular solid. If a representation is unique, then it is easy to determine if two solids are identical since one can just compare their representations.

Accuracy : A representation is said accurate if no approximation is required.

Validness : This means a representation should not create any invalid or impossible solids. More precisely, a representation will not represent an object that does not correspond to a solid.

Closure : Solids will be transformed and used with other operations such as union and intersection. "Closure" means that transforming a valid solid always yields a valid solid.

Compactness and Efficiency : A good representation should be compact enough for saving space and allow for efficient algorithms to determine desired physical characteristics.


Outline


• Raw data• Point cloud• Range image

• Solids• Surfaces


Point cloud Unstructured samples Advantage: simplicity Disadvantage: no information on

adjacency / connectivity


Range image Image: stores a color along each of a set of

regularly-spaced rays in space Range image: stores a depth along each of a set of

regularly-spaced rays in space Obtained using devices known as range scanners

PMD, CamCube 3.0, TOF cameraVivid910, Laser scanner


Range image Image: stores a color along each of a set of

regularly-spaced rays in space Range image: stores a depth along each of a set of

regularly-spaced rays in space Obtained using devices known as range scanners

2.5D range image 2D ear Range image with rendering


Outline


• Raw data• Solids

• Wireframe model• Constructive solid geometry• Voxels

• Surfaces


Wireframe model Wireframe model

The oldest way of representing solids It represents shape of a solid object by its characteristics

lines and points A wireframe model does not have face information A wireframe model consists of two tables, the vertex table

and the edge table. Each entry of the vertex table records a vertex and its coordinate values, while each entry of the edge table has two components giving the two incident vertices of that edge


Wireframe modelFor example, to represent a cube defined by eight vertices and 12 edges, one needs the following tables

Vertex Table

Vertex # x y z

1 1 1 1 2 1 -1 1 3 -1 -1 1 4 -1 1 1 5 1 1 -1 6 1 -1 -1 7 -1 -1 -1 8 -1 1 -1

Edge TableEdge # Start Vertex End Vertex

1 1 2 2 2 3 3 3 4 4 4 1 5 5 6 6 6 7 7 7 8 8 8 5 9 1 5 10 2 6 11 3 7 12 4 8


Wireframe model It is ambiguous

which one?


Outline




• Surfaces


Constructive solid geometry CSG

A CSG solid is constructed from a few primitives with Boolean operators

Primitives: Cuboids(立方体), cylinders(圆柱体), prisms(棱柱), pyramids(角锥体), spheres(球体), cones(圆锥), torus(圆环)

Boolean operators: union, intersection, difference

A+B A^B A-B B-A

Example:


Constructive solid geometryA CSG Example:

we want to design a bracket-like shape with a hole shown on the right-most figure below1. start with two blocks and one cylinder2. two blocks are scaled and one of them is rotated3. The cylinder is scaled 4. These three instantiations are then transformed to their

desired positions5. The final product is obtained by computing the union of the

two blocks and then subtracting from it the cylinder.


Constructive solid geometryA CSG Example:

The design procedure of the above model can be written as an expression:

(trans(Block1) + trans(Block2)) - trans(Cylinder)

This expression can be converted to an expression tree, the CSG Expression, of the design:

Is CSG representation

unique?


Constructive solid geometry Implementation

represent each elementary solid, e.g. cube, as a 3D field of values, negative on the inside and positive outside

The CSG operations of union, intersection, and subtractionthen become simple min/max operations on the 3D fields

After all CSG operations are complete, the volume representation is converted to surfaces for rendering


Constructive solid geometry ImplementationAny object is defined on a unified domain ; its interior and boundary has negative values, while its exterior has positive values

Ω

objA: the positions of its valid closure have negative values; positions of its exterior have positive values;objB: the positions of its valid closure have negative values; positions of its exterior have positive values;

Then, Union (objA, objB) = min (objA, objB)Intersection (objA, objB) = max (objA, objB)Difference (objA, objB) = max(objA, -objB)

confused?

More explanations are needed here


Constructive solid geometry ImplementationAn example to illustrate this in Matlab code is available on the course website!


Constructive solid geometry It is often used in CAD tools


Outline




• Surfaces


Voxels Partition space into uniform grid

Grid cells are called a voxels (like pixels) Store properties of solid object with each voxel

Occupancy Color Density Temperature


Voxel Acquisition Scanning devices

Computed tomography (CT) Magnetic resonance imaging (MRI)

Simulation

Siemens MRI Volume data example


Voxel Acquisition Widely used in medical imaging


Outline



• Mesh• Subdivision• Parametric• Implicit


Mesh


Mesh

Which Part？


Mesh Connected set of polygons (usually triangles) Representation: Vertices, Indexed Face Set

Pros: flexible and computers can render them so quickly. So the vast majority of 3D models today are built as textured polygonal models

Cons: polygons are planar and can only approximate curved surfaces using many polygons


Mesh RepresentationKey elements to represent a mesh?

• Vertex (顶点)• Face (面)• Edge (边)

Main data structures• Face table (边表)• Winged edge (翼边)• ……


FACE TABLEf1

f2

f3

(x1,y1,z1), (x2,y2,z2), (x3,y3,z3)(x2,y2,z2), (x4,y4,z4), (x3,y3,z3)(x2,y2,z2), (x5,y5,z5), (x4,y4,z4)

Face Table (边表)

Each face is represented by vertex coordinates (坐标)• Redundant (冗余的) vertices• No adjacency (邻接) information

f1

f2 f3

(x1,y1,z1)

(x5,y5,z5)

(x3,y3,z3)

(x4,y4,z4)

(x2,y2,z2)


Winged Edge (翼边)Edge-centered: adjacency encoded in edges

(以边为中心)• Adjacent vertexes• Adjacent faces• Adjacent edges

Properties• All adjacencies in O(1) time• A bit extra storage• popular

eF1

F2v2

e11

v1

e22

e21

e12


e2

e1

e2

e1

e3

e5

e4

e2

e1

e5

e3

e6

e2

e5

e4

e3

e1

e7

e4

e7

e6

e3

e6

e4

e5

e7

e7

e6

f1

f2 f3

e1

e4

e5e3

e2

e7

e6

v1

v5

v4

v3

v2

f1

f2

f2

f3

f3

f1

f1

f2

f3

(v1,v3)(v1,v2)(v2,v3)(v3,v4)(v2,v4)(v2,v5)(v4,v5)

Example

VERTEX TABLE

v1

v2

v3

v4

v5

(x1,y1,z1)(x2,y2,z2)(x3,y3,z3)(x4,y4,z4)(x5,y5,z5)

FACE TABLE

f1

f2

f3

EDGE TABLE

e1

e2

e3

e4

e5

e6

e7

11 12 21 22

e1e3e5

e1e6e3e5e6

Winged Edge (翼边)


Comparison

Data structure Face Vertex Edge Adjacency Storage

Face table Yes - - - High

Winged edge - - Yes V-E-F Edge-centered

“F” stands for face, “V” stands for vertex, and “E” stands for edge.

“-” indicates the adjacency is encoded in the data structure.


Mesh Subdivision Coarse mesh & subdivision rule

Define smooth surface as limit of sequence of refinements

…..


Mesh Subdivision Coarse mesh & subdivision rule

Define smooth surface as limit of sequence of refinements


Mesh Simplification• Fine mesh coarse mesh

• Basic function in mesh processing


Mesh Simplification• How?

• Edge collapse


Mesh Simplification• How?

• Vertex removal


Mesh Simplification• More examples


Outline



• Mesh• Subdivision surface• Parametric surface• Implicit surface


Parametric surface A parametric surface is a surface in the Euclidean

space R3 which is defined by a parametric equation with two parameters

( , ) ( , ), ( , ), ( , )r u v x u v y u v z u v=

Examples:


Outline



• Mesh• Subdivision surface• Parametric surface• Implicit surface


Implicit surface Points satisfying

( , , ) 0F x y z =

An example in 2D case (an implicit curve):

( , , ) 0( , , ) 0( , , ) 0

F x y zF x y zF x y z

< = >

In fact

(x, y, z) inside the surface(x, y, z) on the surface(x, y, z) outside the surface


Implicit surfaceAn example

A mechanical model built by using implicit surface tool


Thanks everybody！

Q & A?

lecture 2 3d modeling - tongji universitysse.tongji.edu.cn/jiajinyuan/acg2012fall/lecture 02-3d...

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