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what is octree encodingoctress are hierarchical variant of spatial-occupancy enumeration designed to address that approachs demanding storage
cell-decompositionin cell-decomposition an object can be represented as the sum of cells into which it can be decomposed each cell-decomposition
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primitive instancingin primitive instancing the modeling system defines a set of primitive 3d solid shapes that are relevant to the application area
hybrid sweepit combines linear andor non-linear sweep via set operations in this case two point sets are swept in two different directions and the
non-linear sweepin non-linear sweep the path is a curve described by a higher-order equation quadratic cubic or
linear sweepin linear sweep the path is a linear or circular vector described by a linear most often parametric linear sweep can be divided into
sweep representations the simplest form of sweep is that produced by sweeping a two-dimensional area along an axis perpendicular to its plane this
half-space methodsolid representation is based fundamentally on the notion that a physical object divides an n-dimensional space en into two regions
analytical solid modeling asmasm is closely related to finite element modeling it is developed to aid designers in the arduous task of modeling
name the boolean set operators used in csgthe boolean set operators used are union a b is the set of points that are in a or b intersection a b
constructive solid-geometry methods csgconstructive models represent a solid as a combination of primitive solids this modeling technique combine the
constructive solid geometry csg or c-repa csg model is based on the topological notion that a physical project object can be divided into a set of
manifoldsthe surface of a solid must satisfy some conditions so that the resulting solid is well-behaved this is the so-called manifold condition
tessellated modellers solid modeling this describes a class of simplified boundary-representation modellers which approximate to curved
determine the edge tableeach entry in the edge table contains those information mentioned earlier edge name start vertex and end vertex left face and
the winged-edge representationperhaps the oldest data structure for a b-rep is baumgarts winged-edge data structure it is quite different from that
what is euler operatoronce a polyhedron model is available one might want to edit it by adding or deleting vertices edges and faces to create a new
the euler-poincare formula the euler-poincareacute formula describes the relationship of the number of vertices the number of edges and the number
polyhedra and eulers formulathe b-rep of a polyhedra that are holomorphic to a sphere are topologically valid if they satisfy the following equations
tropical geometric information of solidsa face is surrounded by a set of vertices using the right-handed rule the ordering of these vertices for
geometric information of b-repgeometric information are usually equations of the edges and
topological information of b-rep it provide the relationships among vertices edges and faces similar to that used in a wire-frame model in addition
primitives of b-rep schemethe building blocks for b-rep models are vertexit is a unique point an ordered triplet in spaceedgean edge is a finite
define the boundary representation of solidsboundary model or b-rep model is based on the topological notion that a physical object is bounded by a