Polyhedral Geometry in xGenerative Design

In addition to the exact geometry usually managed in the app, it is possible to use inputs with polyhedral geometries and to manipulate these geometries in xGenerative Design.

This page discusses:

Types of Geometric Modeling

In the app, the geometric definition of objects can be based on two types of modeling.

Exact Geometry

The underlying model of an exact geometry is built on mathematical geometric modeling (Bezier curves, NURBS, rational functions) and on associated topology information. This allows to use all the possibilities of the modeler as well as all the operators available in the app.

Polyhedral Geometry

The underlying model of surfaces and volumes using polyhedral modeler is based on triangular meshes. For polyhedral curves, the underlying model is based on the composition of linear segments.

The basic polyhedral geometry (points, segments, triangles) is completed by the system by associating useful topological information. For example: face boundaries (subset of triangles), or edge edges (set of triangle segments representing sharps edges).

The advantage of this modeling is to be able to use some geometric modeling operators as if they were exact geometries. Operators that support polyhedral geometry are listed below.

Important: Points are both exact and polyhedral geometries.

Representation in the 3D Area

Specific colors are associated with the polyhedral geometries to distinguish them from the exact geometries.



Exact surface
Exact volume
Exact curve
Polyhedral surface
Polyhedral volume
Polyhedral curve

Operators Supporting Polyhedral Geometries

The following operators can be used with polyhedral geometry:

Category Operators
Geometry

Boolean operators on volumes:

  • Add
  • Remove

Transformation operators:

  • Translate by Coordinates
  • Translate Two Points
  • Translate Length Direction
  • Rotate
  • Scale
  • Affinity
  • Symmetry

Other operators:

  • Split
  • Extrude
  • Intersect
  • Center
  • Assemble. For this operator, the union parameter is ineffective when used as input.
  • Project. For this operator, an explicit defined direction is required for the projection of curves.
  • Curve Parallel. For this operator, only planar curves are supported.
  • Trim. For this operator, infinite geometry cannot be used as input.

For more information about Geometry operators, see Geometry.
Measure
  • Distance
  • Area
  • Volume
  • Length
  • Point ratio on Curve
  • IsClosed

For more information about Measure operators, see Measure.
Tip: In the Search box of the Graph Editor, you can use the Polyhedral tag to find operators that can be used with polyhedral geometry. For more information, see About the Search Feature.

Hybrid Modeling

Operators supporting polyhedral geometries and requesting several geometrical inputs let you mix inputs of both geometric models: exact and polyhedral. This use case is called hybrid modeling.

If some inputs are exact and some are polyhedral, all the exact geometries are automatically converted into polyhedral geometries. The result is a polyhedral model.

To improve the performances, you can use the Exact To Polyhedral operator to make the conversion in a single step. For more information, see Exact To Polyhedral.

Additional Operators

Two additional operators are helpful when working with hybrid modeling.

Exact to Polyhedral

This operator converts an exact geometry into a polyhedral geometry, which lets you work faster.

For example, if you use an operator that requires several inputs and if one of the inputs is a polyhedral geometry, the Exact to Polyhedral operator automatically converts all the other input geometries. As a result, the output geometry is always polyhedral.

For more information, see Exact To Polyhedral.

Point on Surface from Center

This operator lets you create points on a polyhedral geometry and on an exact surface.

For more information, see Point on Surface from Center.