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 VRML 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:

• PointSet
• IndexedLineSet
• IndexedFaceSet

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 VRML 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 VRML 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 VRML 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 VRML 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 VRML 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.