toxi.geom
Class Spline2D

java.lang.Object
  extended by toxi.geom.Spline2D

public class Spline2D
extends java.lang.Object

This is a generic 3D B-Spline class for curves of arbitrary length, control handles and patches are created and joined automatically as described here: ibiblio.org/e-notes/ Splines/Bint.htm

Thanks to a bug report by Aaron Meyers (http://universaloscillation.com) the computeVertices(int) method has a slightly changed behaviour from version 0014 onwards. In earlier versions erroneous duplicate points would be added near each given control point, which lead to various weird results.

The new behaviour of the curve interpolation/computation is described in the docs for the computeVertices(int) method below.


Field Summary
 BernsteinPolynomial bernstein
           
 float[] bi
           
 Vec2D[] coeffA
           
static int DEFAULT_RES
           
static float DEFAULT_TIGHTNESS
           
 Vec2D[] delta
           
 java.util.List<Vec2D> pointList
           
 java.util.List<Vec2D> vertices
           
 
Constructor Summary
Spline2D()
          Constructs an empty spline container with default curve tightness.
Spline2D(java.util.List<Vec2D> rawPoints)
           
Spline2D(java.util.List<Vec2D> rawPoints, BernsteinPolynomial b, float tightness)
           
Spline2D(Vec2D[] pointArray)
           
Spline2D(Vec2D[] pointArray, BernsteinPolynomial b, float tightness)
           
 
Method Summary
 Spline2D add(float x, float y)
           
 Spline2D add(ReadonlyVec2D p)
          Adds the given point to the list of control points.
 java.util.List<Vec2D> computeVertices(int res)
           Computes all curve vertices based on the resolution/number of subdivisions requested.
 java.util.List<Vec2D> getDecimatedVertices(float step)
          Computes a list of points along the spline which are uniformly separated by the given step distance.
 java.util.List<Vec2D> getDecimatedVertices(float step, boolean doAddFinalVertex)
          Computes a list of points along the spline which are uniformly separated by the given step distance.
 float getEstimatedArcLength()
           
 int getNumPoints()
          Returns the number of key points.
 java.util.List<Vec2D> getPointList()
           
 float getTightness()
           
 Spline2D setPointList(java.util.List<Vec2D> plist)
          Overrides the current control points with the given list.
 Spline2D setTightness(float tightness)
          Sets the tightness for future curve interpolation calls.
 void updateCoefficients()
           
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

DEFAULT_TIGHTNESS

public static final float DEFAULT_TIGHTNESS
See Also:
Constant Field Values

DEFAULT_RES

public static final int DEFAULT_RES
See Also:
Constant Field Values

pointList

public java.util.List<Vec2D> pointList

vertices

public java.util.List<Vec2D> vertices

bernstein

public BernsteinPolynomial bernstein

delta

public Vec2D[] delta

coeffA

public Vec2D[] coeffA

bi

public float[] bi
Constructor Detail

Spline2D

public Spline2D()
Constructs an empty spline container with default curve tightness. You need to populate the spline manually by using add(ReadonlyVec2D) .


Spline2D

public Spline2D(java.util.List<Vec2D> rawPoints)
Parameters:
rawPoints - list of control point vectors

Spline2D

public Spline2D(java.util.List<Vec2D> rawPoints,
                BernsteinPolynomial b,
                float tightness)
Parameters:
rawPoints - list of control point vectors
b - predefined Bernstein polynomial (good for reusing)
tightness - default curve tightness used for the interpolated vertices setTightness(float)

Spline2D

public Spline2D(Vec2D[] pointArray)
Parameters:
pointArray - array of control point vectors

Spline2D

public Spline2D(Vec2D[] pointArray,
                BernsteinPolynomial b,
                float tightness)
Parameters:
pointArray - array of control point vectors
b - predefined Bernstein polynomial (good for reusing)
tightness - default curve tightness used for the interpolated vertices setTightness(float)
Method Detail

add

public Spline2D add(float x,
                    float y)

add

public Spline2D add(ReadonlyVec2D p)
Adds the given point to the list of control points.

Parameters:
p -
Returns:
itself

computeVertices

public java.util.List<Vec2D> computeVertices(int res)

Computes all curve vertices based on the resolution/number of subdivisions requested. The higher, the more vertices are computed:

(number of control points - 1) * resolution + 1

Since version 0014 the automatic placement of the curve handles can also be manipulated via the setTightness(float) method.

Parameters:
res - the number of vertices to be computed per segment between original control points (incl. control point always at the start of each segment)
Returns:
list of Vec2D vertices along the curve

getDecimatedVertices

public java.util.List<Vec2D> getDecimatedVertices(float step)
Computes a list of points along the spline which are uniformly separated by the given step distance.

Parameters:
step -
Returns:
point list

getDecimatedVertices

public java.util.List<Vec2D> getDecimatedVertices(float step,
                                                  boolean doAddFinalVertex)
Computes a list of points along the spline which are uniformly separated by the given step distance.

Parameters:
step -
doAddFinalVertex - true, if the last vertex computed by computeVertices(int) should be added regardless of its distance.
Returns:
point list

getEstimatedArcLength

public float getEstimatedArcLength()
Returns:
estimated arc length based on summing the individual lengths of the line segments computed with computeVertices(int).

getNumPoints

public int getNumPoints()
Returns the number of key points.

Returns:
the numP

getPointList

public java.util.List<Vec2D> getPointList()
Returns:
the pointList

getTightness

public float getTightness()
Returns:
the spline3d tightness
Since:
0014 (rev.216)
See Also:
setTightness(float)

setPointList

public Spline2D setPointList(java.util.List<Vec2D> plist)
Overrides the current control points with the given list.

Parameters:
plist -
Returns:
itself

setTightness

public Spline2D setTightness(float tightness)
Sets the tightness for future curve interpolation calls. Default value is 0.25. A value of 0.0 equals linear interpolation between the given curve input points. Curve behaviour for values outside the 0.0 .. 0.5 interval is unspecified and becomes increasingly less intuitive. Negative values are possible too and create interesting results (in some cases).

Parameters:
tightness - the tightness value used for the next call to computeVertices(int)
Since:
0014 (rev. 216)

updateCoefficients

public void updateCoefficients()