defining objects - 3d representations surface representations polygon tables 3d curves and curved...

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DEFINING OBJECTS - 3D REPRESENTATIONS Surface representations Polygon tables 3D curves and curved surfaces Sweep representations Constructive solid geometry Octrees

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DEFINING OBJECTS - 3D REPRESENTATIONS

Surface representations

Polygon tables

3D curves and curved surfaces

Sweep representations

Constructive solid geometry

Octrees

Two classes of representations

Surface

Solid

Surface representations

• Polygon surfaces

Surface representations

Object triangulation

Succession of models

Wireframe Surface patch

Surface patch Surface shading

Surface representation

SurfaceVertex

Edge

Vertices

V1

V2V3

V4

V5

V6 V7

V8

Wire-frameV1

V2V3

V4

V5

V6 V7

V8

V1

V2V3

V4

V5

V6 V7

V8

V1

V2V3

V4

V5

V6 V7

V8

Surface

V1

V2V3

V4

V5

V6 V7

V8

V2

V1

V2V3

V4

V5

V6 V7

V8

V2

Vertex table

VERTEX TABLE

V1: x1 y1 z1V2: x2 y2 z2V3: x3 y3 z3V4: x4 y4 z4V5: x5 y5 z5V6: x6 y6 z6V7: x7 y7 z7V8: x8 y8 z8

EDGE TABLE

E1: V1 V2E2: V2 V3E3: V3 V4E4: V4 V1E5: V5 V6E6: V6 V7E7: V7 V8E8: V8 V5E9: V1 V5E10: V2 V6E11: V3 V7E12: V4 V8

SURFACE TABLE

S1: E1 E2 E3 E4S2: E5 E6 E7 E8S3: E1 E10 E5 E9S4: E2 E11 E6 E10S5: E3 E12 E7 E11S6: E4 E9 E8 E12

Define vertex table(vertices and edges)

2 4 6 8

2

4

6

8

X

Y Z

2

V1 V2

V3V4

V5 V6

V7V8

Consistency checking

• every vertex is listed as an endpoint of at least two lines

• every polygon is closed• each polygon has at least one shared edge• if edge table contains pointers to polygons

Hierarchical definitions

– interaction: groups of primitives can be interactively manipulated together, irrespective of a method of construction.

– storage efficiency: definition of repeated symbol needs to be stored only once

– common visual properties: groups of primitives can be given the same attributes, for example colour, transparency, visibility etc.

– common transformation: groups of primitives can be all transformed together (for example rotated)

Advanced representations for curves and curved surfaces (3D)

• parametric equations• Bézier curves and surfaces• splines and spline surfaces• B-splines• ß-splines• fractal surfaces

Advanced representations for solids

• Sweep representations• Constructive Solid Geometry (CSG)• Octrees

Sweep representations

Sweep representations

Constructive solid geometry

A B A - B A B

Volume = set of points

Octrees

0 1

23

0 1 2 3

0 1 2 3

0 1 2 3

0 1

23

Octrees

0 1

23

45

6

7

Define vertex table(vertices and edges)

2 4 6 8

2

4

6

8

X

Y Z

2

V1 V2

V3V4

V5 V6

V7V8

V11 V12

V13

V14

V15 V16

V17V18

V9

V19

V20

V10