New Graphical Modelskucg.korea.ac.kr/.../CNCE340/tutor/02GraphicalModels.pdf · 2002. 1. 16. ·...

Graphics

Graphics Lab @ Korea Universitykucg.korea.ac.kr

Graphical Models

고려대학교 컴퓨터 그래픽스 연구실

Overview

3D Geometric PrimitivesPointLinePlanePolygonSphere

3D Object RepresentationsRaw DataSurfacesSolidsOpenGL Primitives

3D Geometric Primitives

PointLinePlanePolygonSphereEtc.

3D Point

Specifies a LocationRepresented by three coordinatesInfinitely small

typedef struct{

Coordinate x;

Coordinate y;

Coordinate z;

} Point;

(x, y, z)

3D Vector

Specifies a Direction and a MagnitudeRepresented by three coordinatesMagnitude ||v||=sqrt(dxdx + dydy +dzdz)Has no location

Dot product of two 3D vectorV1 V2 = dx1dx2 + dy1dy2 + dz1dz2V1 V2 = ||V1||||V2|| cos( )

typedef struct{Coordinate x;Coordinate y;Coordinate z;

} Vector;

⋅⋅ θ

(dx1, dy1, dz1)

(dx2, dy2, dz2)

3D Line

Line segment with both endpoints at infinityParametric Representation

P=P1+tV, ( )∞<<∞− ttypedef struct{

Point P1;Vector V;

} Line;P1

3D Ray

Line segment with one endpoint at infinityParametric Representation

P=P1+tV, ( )∞<<= t0typedef struct{

Point P1;Vector V;

} Ray;P1

3D Line Segment

Specifies a linear combination of two pointsParametric Representation

P=P1 + t(P2 - P1), ( )10 ≤≤ t

typedef struct{Point P1;Point P2;

} Segment;

3D Plane

Specifies a linear combination of three pointsImplicit Representation

P N + d = 0, orax + by + cz + d = 0

typedef struct{Vector N;Distance d;

} Plane;

⋅N=(a, b, c)

Origin

3D Polygon

Area “inside” a sequence of coplanar pointsTriangleQuadrilateralConvexStar-shapedConcaveSelf-Intersecting Hole

typedef struct{Point *Points;int npoints;

} Polygon; Points are in counter-clockwise order

3D Sphere

All points at distance “r” from a center (cx, cy, cz) Implicit Representation

(x-cx)2 + (y-cy)2 + (z-cz) 2 = r 2

Parametric Representationx= r sin( ) cos( )y= r sin( ) sin( )z= r cos( )

φ θφ

r(cx, cy, cz)

3D Object Representations

Raw DataPoint CloudRange ImagePolygon Soup

SurfacesMesh, Subdivision, Parametric, Implicit

SolidsVoxel, BSP tree, CSG, Sweep

Point Cloud

Unstructured Set of 3D Point SamplesAcquired from 3D scanners, computer vision, etc

Range Image

Set of 3D Points Mapping to Pixels of Depth Image

Acquired from range scanner

Range Image Tessellation Range Surface

Polygon Soup

Unstructured Set of PolygonsCreated with interactive modeling systems

Raw DataPoint cloud, Range image, Polygon soup

SurfacesMeshSubdivisionParametricImplicit

SolidsVoxel, BSP tree, CSG, Sweep

Connected Set of Polygons (Usually Triangles)May not be closed

Subdivision Surfaces

Coarse Mesh & Subdivision RuleDefine smooth surface as limit of sequence of refinements

Parametric Surfaces

Tensor Product Spline PatchesCareful constraints to maintain continuity

Implicit Surface

Points satisfying: F(x,y,z) = 0

Polygonal Model Implicit Model

Raw DataPoint cloud, Range image, Polygon soup

SurfacesMesh, Subdivision, Parametric, Implicit

SolidsVoxelBSP treeCSGSweep

Voxels

Uniform Grid of Volumetric SamplesAcquired from CAT, MRI, etc.

BSP Tree

Binary Space Partition with Solid Cells LabeledConstructed from polygonal representations

Object

Binary Spatial Partition

BSP Tree

Hierarchy of Boolean Set Operations (Union, Difference, Intersect) Applied to Simple Shapes

Solid Swept by Curve Along Trajectory

Constructing a Torus Using Rotational Sweep

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_POINTS

glBegin(GL_POINTS);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_LINES

glBegin(GL_LINES);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_LINE_STRIP

glBegin(GL_LINE_STRIP);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_LINE_LOOP

glBegin(GL_LINE_LOOP);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_TRIANGLES

glBegin(GL_TRIANGLES);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_QUADS

glBegin(GL_QUADS);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_POLYGON

glBegin(GL_POLYGON);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);glVertex3f(v5x, v5y, v5z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_TRIANGLE_STRIP

glBegin(GL_TRIANGLE_STRIP);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);glVertex3f(v5x, v5y, v5z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_TRIANGLE_FAN

glBegin(GL_TRIANGLE_FAN);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);glVertex3f(v5x, v5y, v5z);

glEnd();v1

OpenGL Primitives

Taxonomy of 2D Object RepresentationsGL_QUAD_STRIP

glBegin(GL_QUAD_STRIP);glVertex3f(v1x, v1y, v1z);glVertex3f(v2x, v2y, v2z); glVertex3f(v3x, v3y, v3z);glVertex3f(v4x, v4y, v4z);glVertex3f(v5x, v5y, v5z);glVertex3f(v6x, v6y, v6z);

glEnd();

OpenGL Primitives

Taxonomy of 2D Object Representations2D Example

OpenGL Primitives

Taxonomy of 3D Object Representationsvoid glutSolidCube(GLdouble size)

void glutWireCube(GLdouble size)

void glutSolidTetrahedron()

void glutWireTetrahedron()

OpenGL Primitives

Taxonomy of 3D Object Representationsvoid glutSolidSphere(GLdouble radius, GLint slices, GLint stacks)

void glutWireSphere (GLdouble radius, GLint slices, GLint stacks)

OpenGL Primitives

Taxonomy of 3D Object Representationsvoid glutSolidTorus(GLdouble innerRadius, GLdouble outerRadius,GLint nsides, GLint rings)

void glutWireTorus(GLdouble innerRadius, GLdouble outerRadius,GLint nsides, GLint rings)

OpenGL Primitives

Taxonomy of 3D Object Representationsvoid glutSolidCone(GLdouble base, GLdouble height,GLint slices, GLint stacks)

void glutWireCone(GLdouble base, GLdouble height,GLint slices, GLint stacks)

OpenGL Primitives

Taxonomy of 3D Object Representationsvoid glutSolidcosahedron()

void glutWirecosahedron()

void glutSolidTeapot(GLdouble size)

void glutWireTeapot(GLdouble size)

OpenGL Primitives

Taxonomy of 3D Object Representations3D Example

Summary

Taxonomy of 3D Object Representations

Discrete Continuous

Combinational Functional

MeshSubdivision

BSP Tree BezierB-Spline

Algebraic

Topological Set Membership Parametric Implicit

New Graphical Modelskucg.korea.ac.kr/.../CNCE340/tutor/02GraphicalModels.pdf · 2002. 1. 16. ·...

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