Package arc.math.geom

Class BSpline<T extends Vector<T>>

java.lang.Object
arc.math.geom.BSpline<T>
All Implemented Interfaces:
Path<T>
public class BSpline<T extends Vector<T>> extends Object implements Path<T>

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    boolean
    continuous
     
    T[]
    controlPoints
     
    int
    degree
     
    Seq<T>
    knots
     
    int
    spanCount
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    BSpline()
     
    BSpline(T[] controlPoints, int degree, boolean continuous)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    float
    approximate(T v)
     
    float
    approximate(T in, int near)
     
    float
    approximate(T in, int start, int count)
     
    float
    approxLength(int samples)
     
    static <T extends Vector<T>>
    T
    calculate(T out, float t, T[] points, int degree, boolean continuous, T tmp)
    Calculates the n-degree b-spline value for the given position (t).
    static <T extends Vector<T>>
    T
    calculate(T out, int i, float u, T[] points, int degree, boolean continuous, T tmp)
    Calculates the n-degree b-spline value for the given span (i) at the given position (u).
    static <T extends Vector<T>>
    T
    cubic(T out, float t, T[] points, boolean continuous, T tmp)
    Calculates the cubic b-spline value for the given position (t).
    static <T extends Vector<T>>
    T
    cubic(T out, int i, float u, T[] points, boolean continuous, T tmp)
    Calculates the cubic b-spline value for the given span (i) at the given position (u).
    static <T extends Vector<T>>
    T
    cubic_derivative(T out, float t, T[] points, boolean continuous, T tmp)
    Calculates the cubic b-spline derivative for the given position (t).
    static <T extends Vector<T>>
    T
    cubic_derivative(T out, int i, float u, T[] points, boolean continuous, T tmp)
    Calculates the cubic b-spline derivative for the given span (i) at the given position (u).
    static <T extends Vector<T>>
    T
    derivative(T out, float t, T[] points, int degree, boolean continuous, T tmp)
    Calculates the n-degree b-spline derivative for the given position (t).
    static <T extends Vector<T>>
    T
    derivative(T out, int i, float u, T[] points, int degree, boolean continuous, T tmp)
    Calculates the n-degree b-spline derivative for the given span (i) at the given position (u).
    T
    derivativeAt(T out, float t)
     
    T
    derivativeAt(T out, int span, float u)
     
    float
    locate(T v)
     
    int
    nearest(T in)
     
    int
    nearest(T in, int start, int count)
     
    BSpline
    set(T[] controlPoints, int degree, boolean continuous)
     
    T
    valueAt(T out, float t)
     
    T
    valueAt(T out, int span, float u)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • controlPoints

      public T extends Vector<T>[] controlPoints

    • knots

      public Seq<T extends Vector<T>> knots

    • degree

      public int degree

    • continuous

      public boolean continuous

    • spanCount

      public int spanCount

  • Constructor Details

    • BSpline

      public BSpline()

    • BSpline

      public BSpline(T[] controlPoints, int degree, boolean continuous)

  • Method Details

    • cubic

      public static <T extends Vector<T>> T cubic(T out, float t, T[] points, boolean continuous, T tmp)
      Calculates the cubic b-spline value for the given position (t).
      Parameters:
      out - The Vector to set to the result.
      t - The position (0<=t<=1) on the spline
      points - The control points
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • cubic_derivative

      public static <T extends Vector<T>> T cubic_derivative(T out, float t, T[] points, boolean continuous, T tmp)
      Calculates the cubic b-spline derivative for the given position (t).
      Parameters:
      out - The Vector to set to the result.
      t - The position (0<=t<=1) on the spline
      points - The control points
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • cubic

      public static <T extends Vector<T>> T cubic(T out, int i, float u, T[] points, boolean continuous, T tmp)
      Calculates the cubic b-spline value for the given span (i) at the given position (u).
      Parameters:
      out - The Vector to set to the result.
      i - The span (0<=i<spanCount) spanCount = continuous ? points.length : points.length - 3 (cubic degree)
      u - The position (0<=u<=1) on the span
      points - The control points
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • cubic_derivative

      public static <T extends Vector<T>> T cubic_derivative(T out, int i, float u, T[] points, boolean continuous, T tmp)
      Calculates the cubic b-spline derivative for the given span (i) at the given position (u).
      Parameters:
      out - The Vector to set to the result.
      i - The span (0<=i<spanCount) spanCount = continuous ? points.length : points.length - 3 (cubic degree)
      u - The position (0<=u<=1) on the span
      points - The control points
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • calculate

      public static <T extends Vector<T>> T calculate(T out, float t, T[] points, int degree, boolean continuous, T tmp)
      Calculates the n-degree b-spline value for the given position (t).
      Parameters:
      out - The Vector to set to the result.
      t - The position (0<=t<=1) on the spline
      points - The control points
      degree - The degree of the b-spline
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • derivative

      public static <T extends Vector<T>> T derivative(T out, float t, T[] points, int degree, boolean continuous, T tmp)
      Calculates the n-degree b-spline derivative for the given position (t).
      Parameters:
      out - The Vector to set to the result.
      t - The position (0<=t<=1) on the spline
      points - The control points
      degree - The degree of the b-spline
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • calculate

      public static <T extends Vector<T>> T calculate(T out, int i, float u, T[] points, int degree, boolean continuous, T tmp)
      Calculates the n-degree b-spline value for the given span (i) at the given position (u).
      Parameters:
      out - The Vector to set to the result.
      i - The span (0<=i<spanCount) spanCount = continuous ? points.length : points.length - degree
      u - The position (0<=u<=1) on the span
      points - The control points
      degree - The degree of the b-spline
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • derivative

      public static <T extends Vector<T>> T derivative(T out, int i, float u, T[] points, int degree, boolean continuous, T tmp)
      Calculates the n-degree b-spline derivative for the given span (i) at the given position (u).
      Parameters:
      out - The Vector to set to the result.
      i - The span (0<=i<spanCount) spanCount = continuous ? points.length : points.length - degree
      u - The position (0<=u<=1) on the span
      points - The control points
      degree - The degree of the b-spline
      continuous - If true the b-spline restarts at 0 when reaching 1
      tmp - A temporary vector used for the calculation
      Returns:
      The value of out

    • set

      public BSpline set(T[] controlPoints, int degree, boolean continuous)

    • valueAt

      public T valueAt(T out, float t)
      Specified by:
      valueAt in interface Path<T extends Vector<T>>
      Returns:
      The value of the path at t where 0<=t<=1

    • valueAt

      public T valueAt(T out, int span, float u)
      Returns:
      The value of the spline at position u of the specified span

    • derivativeAt

      public T derivativeAt(T out, float t)
      Specified by:
      derivativeAt in interface Path<T extends Vector<T>>

    • derivativeAt

      public T derivativeAt(T out, int span, float u)
      Returns:
      The derivative of the spline at position u of the specified span

    • nearest

      public int nearest(T in)
      Returns:
      The span closest to the specified value

    • nearest

      public int nearest(T in, int start, int count)
      Returns:
      The span closest to the specified value, restricting to the specified spans.

    • approximate

      public float approximate(T v)
      Specified by:
      approximate in interface Path<T extends Vector<T>>
      Returns:
      The approximated value (between 0 and 1) on the path which is closest to the specified value. Note that the implementation of this method might be optimized for speed against precision, see Path.locate(Object) for a more precise (but more intensive) method.

    • approximate

      public float approximate(T in, int start, int count)

    • approximate

      public float approximate(T in, int near)

    • locate

      public float locate(T v)
      Specified by:
      locate in interface Path<T extends Vector<T>>
      Returns:
      The precise location (between 0 and 1) on the path which is closest to the specified value. Note that the implementation of this method might be CPU intensive, see Path.approximate(Object) for a faster (but less precise) method.

    • approxLength

      public float approxLength(int samples)
      Specified by:
      approxLength in interface Path<T extends Vector<T>>
      Parameters:
      samples - The amount of divisions used to approximate length. Higher values will produce more precise results, but will be more CPU intensive.
      Returns:
      An approximated length of the spline through sampling the curve and accumulating the euclidean distances between the sample points.