Class BezierCap

java.lang.Object
org.bzdev.geom.BezierCap
All Implemented Interfaces:
Shape3D

public class BezierCap extends Object implements Shape3D
A 3D shape consisting of a 'center' point connecting to a path using a sequence of Bezier triangles. The path will typically be a boundary of some other shape. The shape of this object is determined by the center point, a vector defining a direction more or less perpendicular to the boundary, and a height relative to the center point and the direction of the vector.
  • Constructor Details

    • BezierCap

      public BezierCap(Path3D boundary, double height, boolean cmode)
      Constructor. When cmode is false, the spokes will set the tangent at the center point to be perpendicular to this shape's vector and the tangent at the boundary to be parallel to this shape's vector. At both of these end points, the second derivative vanishes. The center point is computed by using findCenter(Path3D) with the boundary as its argument. The vector is computed using findVector(Path3D,Point3D) with the boundary and the center point as its arguments.
      Parameters:
      boundary - the boundary
      height - the height above the boundary for the central point of this shape.
      cmode - true if the spokes should be circular; false if they should be a Bezier curve that is as 'flat' as possible except at a bend
    • BezierCap

      public BezierCap(Path3D boundary, Point3D center, double height, boolean cmode)
      Constructor given a center point. When cmode is false, the spokes will set the tangent at the center point to be perpendicular to this shape's vector and the tangent at the boundary to be parallel to this shape's vector. At both of these end points, the second derivative vanishes. The vector is computed using findVector(Path3D,Point3D) with the boundary and the center point as its arguments.
      Parameters:
      boundary - the boundary
      center - the center point
      height - the height above the boundary for the central point of this shape.
      cmode - true if the spokes should be circular; false if they should be a Bezier curve that is as 'flat' as possible except at a bend
    • BezierCap

      public BezierCap(Path3D boundary, Point3D center, double[] vector, double height, boolean cmode)
      Constructor given a center point and a vector. When cmode is false, the spokes will set the tangent at the center point to be perpendicular to this shape's vector and the tangent at the boundary to be parallel to this shape's vector. At both of these end points, the second derivative vanishes.
      Parameters:
      boundary - the boundary
      center - the center point
      vector - a vector assumed to be perpendicular to the plane containing the boundary (or an approximation to such a plane, particularly if one does not exist)
      height - the height above the boundary for the central point of this shape.
      cmode - true if the spokes should be circular; false if they should be a Bezier curve that is as 'flat' as possible except at a bend
    • BezierCap

      public BezierCap(PathIterator3D pit, Point3D center, double[] vector, double height, boolean cmode)
      Constructor given a path iterator for the boundary. When cmode is false, the spokes will set the tangent at the center point to be perpendicular to this shape's vector and the tangent at the boundary to be parallel to this shape's vector. At both of these end points, the second derivative vanishes.
      Parameters:
      pit - the path iterator for the boundary
      center - the center point
      vector - a vector assumed to be perpendicular to the plane containing the boundary (or an approximation to such a plane, particularly if one does not exist)
      height - the height above the boundary for the central point of this shape.
      cmode - true if the spokes should be circular; false if they should be a Bezier curve that is as 'flat' as possible except at a bend
  • Method Details

    • findCenter

      public static Point3D findCenter(Path3D boundary)
      Find a center point given a boundary. The value returned is that for the center of mass of a line with a uniform density.
      Parameters:
      boundary - the boundary
      Returns:
      the center point; null if the path length of the boundary is zero (e.g., the boundary is empty)
    • findVector

      public static double[] findVector(Path3D boundary, Point3D center)
      Find a vector roughly perpendicular to a boundary, given a center point. The value returned is the average over the boundary of the cross product of a tangent vector to the boundary and a vector from the center point to the boundary, where the tangent vector is of unit length. When the boundary is a 'hole' in a surface, the vector will point in the direction of surface's orientation (boundaries when viewed from the 'outside' of the surface are represented by clockwise curves in this case).
      Parameters:
      boundary - the boundary
      center - the center point
      Returns:
      the vector
    • reverseOrientation

      public void reverseOrientation(boolean reverse)
      Change the orientation of the Bézier triangles associated with this object. This method affects the orientation of triangles provided by iterators. It does not change the values returned by calling methods such as .
      Parameters:
      reverse - true if the orientation is the reverse of the one that was initially defined; false if the orientation is the same as the one that was initially defined.
    • isReversed

      public boolean isReversed()
      Determine if the orientation for this grid is reversed.
      Returns:
      true if the orientation is reversed; false if not
    • setColor

      public void setColor(Color c)
      Set the default color for this shape.
      Parameters:
      c - the color
    • setColor

      public void setColor(int i, Color c)
      Set the color for a Bézier triangle specified by an index
      Parameters:
      i - the index
      c - the color
    • getColor

      public Color getColor()
      Get the default color for this shape. This is the color for the shape, excluding Bézier triangles for which an explicit color has been specified.
      Returns:
      the color
    • getColor

      public Color getColor(int i)
      Get the color for this shape given an index. This is the color for the shape, excluding Bézier triangles for which an explicit color has been specified. When a color for a specific index has been provided, that color is returned; otherwise the default color (if any) is returned.
      Parameters:
      i - the index of a Bézier triangle.
      Returns:
      the color
    • setCP111

      public void setCP111(int i, double[] coords) throws IllegalArgumentException
      Set the inner control point of a Bézier triangle.
      Parameters:
      i - the index of a Bézier triangle.
      coords - a vector of length 3 giving the control point that is not on the Bézier triangle's edge, with coords[0] containing the X value, coords[1] containing the Y value, and coords[2] containing the Z value.
      Throws:
      IllegalArgumentException
    • setSpoke

      public void setSpoke(int i, double[] coords) throws IllegalArgumentException
      Set the intermediate control points for a spoke. Each spoke is a cubic Bézier curve starting at the center point, followed by two control points, and ending on a point on the boundary. The first intermediate control point is specified by coords[0], coords[1], and coords[2]. The second intermediate control point is specified by coords[3], coords[4], and coords[5].
      Parameters:
      i - the index of a Bézier triangle.
      coords - an array of length 6 (or more) containing the control points.
      Throws:
      IllegalArgumentException
    • print

      public void print() throws IOException
      Print this object's control points.
      Throws:
      IOException - an IO error occurred
    • print

      public void print(Appendable out) throws IOException
      Print this object's control points, specifying an output.
      Parameters:
      out - the output
      Throws:
      IOException - an IO error occurred
    • print

      public void print(String prefix) throws IOException
      Print this object's control points, specifying a prefix. Each line will start with the prefix (typically some number of spaces).
      Parameters:
      prefix - the prefix
      Throws:
      IOException - an IO error occurred
    • print

      public void print(String prefix, Appendable out) throws IOException
      Print this object's control points, specifying a prefix and output. Each line will start with the prefix (typically some number of spaces).
      Parameters:
      prefix - the prefix
      out - the output
      Throws:
      IOException - an IO error occurred
    • setRadialTessellation

      public void setRadialTessellation(int level)
      Set the radial tessellation level. Increasing the level by 1 doubles the number of segments in the radial direction.
      Parameters:
      level - the tessellation level
    • getRadialTessellation

      public int getRadialTessellation()
      Get the radial tessellation level
      Returns:
      the radial tesselation level;
    • getSurfaceIterator

      public SurfaceIterator getSurfaceIterator(Transform3D tform)
      Description copied from interface: Shape3D
      Get a surface iterator for this Shape3D. The surface iterator will represent the shape as a sequence of Bézier patches and Bézier triangles, with the order of the sequence arbitrary.

      Unless the transform is an affine transform, the transformation is not exact. In this case, the patches and triangles that constitute the surface should be small enough that the transform can be approximated by an affine transform over the region containing the control points.

      Specified by:
      getSurfaceIterator in interface Shape3D
      Parameters:
      tform - a transform to apply to each control point; null for the identity transform
      Returns:
      a surface iterator
    • getSurfaceIterator

      public final SurfaceIterator getSurfaceIterator(Transform3D tform, int level)
      Description copied from interface: Shape3D
      Get a surface iterator for this Shape3D, subdividing the surface. The surface iterator will represent the shape as a sequence of Bézier patches and Bézier triangles, with the order of the sequence arbitrary.

      Unless the transform is an affine transform, the transformation is not exact. In this case, the patches and triangles that constitute the surface after each is subdivided should be small enough that the transform can be approximated by an affine transform over the region containing the control points.

      Specified by:
      getSurfaceIterator in interface Shape3D
      Parameters:
      tform - a transform to apply to each control point; null for the identity transform
      level - the number of levels of partitioning (each additional level splits the previous level into quarters)
      Returns:
      a surface iterator
    • getBoundary

      public Path3D getBoundary()
      Description copied from interface: Shape3D
      Get the boundary for this Shape3D. For a closed surface, the boundary will be an empty path.

      Typically, a boundary will consist of a series of distinct closed subpaths. Subpaths are separated by segments whose type is {link PathIterator3D#SEG_MOVETO}. For a closed manifold, the boundary will be an empty path.

      Specified by:
      getBoundary in interface Shape3D
      Returns:
      the boundary of this surface; null if a boundary cannot be computed
      See Also:
    • isWellFormed

      public boolean isWellFormed()
      Determine if this BezierCap is well formed.
      Returns:
      true if the grid is well formed; false otherwise
    • isWellFormed

      public boolean isWellFormed(Appendable out)
      Determine if this BezierCap is well formed, logging error messages to an Appendable.
      Parameters:
      out - an Appendable for logging error messages
      Returns:
      true if the grid is well formed; false otherwise
    • getComponent

      public Shape3D getComponent(int i) throws IllegalArgumentException
      Description copied from interface: Shape3D
      Get a component of this shape. Components are connected shapes - surfaces for which every point can connect to any other point. The components are referenced by an index, specified as an integer in the range [0,n), where n is the number of manifold components. If n is zero, no index is valid.
      Specified by:
      getComponent in interface Shape3D
      Parameters:
      i - the component's index
      Returns:
      a model containing the specified component
      Throws:
      IllegalArgumentException - the argument is out of range
      See Also:
    • getBounds

      public Rectangle3D getBounds()
      Description copied from interface: Shape3D
      Get a bounding rectangular cuboid for a 3D shape. The edges will be aligned with the X, Y and Z axes. The cuboid created may not be the smallest one possible (for example, shapes defined by Bézier surfaces may just use the control points to determine the cuboid as the convex hull for the control points includes all of the surface for parameters in the normal range [0,1]).
      Specified by:
      getBounds in interface Shape3D
      Returns:
      a bounding rectangular cuboid for this Shape3D; null if the shape does not contain any points
    • isClosedManifold

      public boolean isClosedManifold()
      Description copied from interface: Shape3D
      Determine if this Shape3D is a closed two-dimensional manifold.
      Specified by:
      isClosedManifold in interface Shape3D
      Returns:
      true if the surface is a closed two-dimensional manifold; false otherwise
    • isOriented

      public boolean isOriented()
      Description copied from interface: Shape3D
      Determine if a surface is oriented.
      Specified by:
      isOriented in interface Shape3D
      Returns:
      true if the surface has an orientation; false if it does not
    • numberOfComponents

      public int numberOfComponents()
      Description copied from interface: Shape3D
      Get the number of components for this shape. Components are connected shapes - surfaces for which every point can connect to any other point.
      Specified by:
      numberOfComponents in interface Shape3D
      Returns:
      the number of components for this shape