Building Shapes out of Points, Lines, and Faces

Motivation

Complex shapes are hard to build with primitive shapes:

  • TerrainAnimals
  • Plants
  • Machinery

Instead, build shapes out of atomic components:

  • Points, lines, and faces

Building shapes using coordinates

Shape building is like a 3-D connect-the-dots game:

  • Place dots at 3-D locations
  • Connect-the-dots to form shapes

A coordinate specifies a 3-D dot location. Measured relative to a coordinate system origin. A geometry node specifies how to connect the dots.

Syntax: Coordinate

A Coordinate node contains a list of coordinates for use in building a shape.

XML Encoding

<!-- X Y Z -->
<Coordinate
    point='2.0 1.0 3.0, 4.0 2.5 5.3, ...'/>

Classic Encoding

Coordinate {
  point [
   #X   Y   Z
    2.0 1.0 3.0,
    4.0 2.5 5.3,
    ...
  ]
}

Using geometry coordinates

Build coordinate-based shapes using geometry nodes:

For all three nodes, use a Coordinate node as the value of the coord field.

Syntax: PointSet

A PointSet geometry node creates geometry out of points:

  • One point (a dot) is placed at each coordinate

XML Encoding

<Shape>
  <Appearance><!-- ... --></Appearance>
  <PointSet>
    <Coordinate
        point='...'/>
  </PointSet>
</Shape>

Classic Encoding

Shape {
  appearance Appearance { ... }
  geometry PointSet {
    coord Coordinate {
      point [  ...  ]
    }
  }
}

Syntax: IndexedLineSet

An IndexedLineSet geometry node creates geometry out of lines:

  • A straight line is drawn between pairs of selected coordinates

XML Encoding

<Shape>
  <Appearance><!-- ... --></Appearance>
  <IndexedLineSet
      coordIndex='...'>
    <Coordinate>
        point='...'/>
  </IndexedLineSet>
</Shape>

Classic Encoding

Shape {
  appearance Appearance { ... }
  geometry  IndexedLineSet {
    coordIndex [ ... ]
    coord Coordinate {
      point [ ... ]
    }
  }
}

Using line set coordinate indexes

Each coordinate in a Coordinate node is implicitly numbered

  • Index 0 is the first coordinate
  • Index 1 is the second coordinate, etc.

To build a line shape:

  • Make a list of coordinates, using their indexes
  • List coordinate indexes in the coordIndex field of the IndexedLineSet node

A line is drawn between pairs of coordinate indexes:

  • -1 marks a break in the line
  • A line is not automatically drawn from the last index back to the first
   
coordIndex [ 1, 0, 3, 8, -1, 5, 9, 0, -1 ]  
1, 0, 3, 8, Draw line from 1 to 0 to 3 to 8
-1, End line, start next
5, 9, 0 Draw line from 5 to 9 to 0

Syntax: IndexedFaceSet

An IndexedFaceSet geometry node creates geometry out of faces:

  • A flat face (polygon) is drawn using an outline specified by coordinate indexes

XML Encoding

<Shape>
  <Appearance><!-- ... --></Appearance>
  <IndexedFaceSet
      coordIndex='...'>
    <Coordinate>
        point='...'/>
  </IndexedFaceSet>
</Shape>

Classic Encoding

Shape {
  appearance Appearance { ... }
  geometry IndexedFaceSet {
    coordIndex [ ... ]
    coord Coordinate {
      point [  ...  ]
    }
  }
}

Using face set coordinate index lists

To build a face shape

  • Make a list of coordinates, using their indexes
  • List coordinate indexes in the coordIndex field of the IndexedFaceSet node

A triangle is drawn connecting sequences of coordinate indexes:

  • -1 marks a break in the sequence
  • Each face is automatically closed, connecting the last index back to the first
   
coordIndex [ 1, 0, 3, 8, -1, 5, 9, 0, -1 ]  
1, 0, 3, 8 Draw face from 1 to 0 to 3 to 8 to 1
-1, End face, start next
5, 9, 0 Draw face from 5 to 9 to 0 to 5
-1 End face

Syntax: IndexedFaceSet

An IndexedFaceSet geometry node creates geometry out of faces:

  • solid - shape is solid
  • ccw - faces are counter-clockwise
  • convex - faces are convex

XML Encoding

<Shape>
  <Appearance><!-- ... --></Appearance>
  <IndexedFaceSet
      solid='true'
      ccw='true'
      convex='true'
      coordIndex='...'>
    <Coordinate ... />
  </IndexedFaceSet>
</Shape>

Classic Encoding

Shape {
  appearance Appearance { ... }
  geometry IndexedFaceSet {
    solid TRUE
    ccw TRUE
    convex TRUE
    coordIndex [ ... ]
    coord Coordinate { ... }
  }
}

Using shape control

A solid shape is one where the insides are never seen:

  • If never seen, don’t attempt to draw them
  • When solid TRUE, the back sides (inside) of faces are not drawn

The front of a face has coordinates in counter-clockwise order:

  • When ccw FALSE, the other side is the front

Faces are assumed to be convex

  • When convex FALSE, concave faces are automatically broken into multiple convex faces

Syntax: CoordinateInterpolator

A CoordinateInterpolator node describes a coordinate path:

  • keys - key fractions
  • keyValues - key coordinate lists (X, Y, Z lists)

XML Encoding

<CoordinateInterpolator
    key='0.0, ...'
    keyValue='0.0 1.0 0.0, ...'/>

Classic Encoding

CoordinateInterpolator {
  key [ 0.0, ... ]
  keyValue [ 0.0 1.0 0.0, ... ]
}

Typically route into a Coordinate node’s set_point input.

Interpolating coordinate lists

A CoordinateInterpolator node interpolates lists of coordinates:

  • Each output is a list of coordinates

If n output coordinates are needed for t fractional times:

  • n × t coordinates are needed in the key value list

Summary

  • Shapes are built by connecting together coordinates
  • Coordinates are listed in a Coordinate node
  • Coordinates are implicitly numbers starting at 0
  • Coordinate index lists give the order in which to use coordinates

The PointSet node draws a dot at every coordinate:

  • The coord field value is a Coordinate node

The IndexedLineSet node draws lines between coordinates:

  • The coord field value is a Coordinate node
  • The coordIndex field value is a list of coordinate indexes

The IndexedFaceSet node draws faces outlined by coordinates:

  • The coord field value is a Coordinate node
  • The coordIndex field value is a list of coordinate indexes

The CoordinateInterpolator node converts times to coordinates.