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 WireframeSurface patch
Surface patch Surface shading
Surface representation Surface Vertex Edge
Vertices
Wire-frame
Surface V1 V2 V3 V4 V5 V6V7 V8 V2 V1 V2 V3 V4 V5 V6V7 V8 V2
Vertex table
Define vertex table (vertices and edges) X Y Z 2 V1 V2 V3 V4 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
Constructive solid geometry A B A - B A B Volume = set of points
Octrees
Define vertex table (vertices and edges) X Y Z 2 V1 V2 V3 V4 V5 V6 V7V8 V11 V12 V13 V14 V15V16 V17V18 V9 V19 V20 V10