Package org.djutils.draw

Class Transform3d

java.lang.Object
org.djutils.draw.Transform3d
All Implemented Interfaces:
Cloneable
public class Transform3d extends Object implements Cloneable
Transform3d contains a MUTABLE transformation object that can transform points (x,y,z) based on e.g, rotation and translation. It uses an affine transform matrix that can be built up from different components (translation, rotation, scaling, reflection, shearing).

Copyright (c) 2020-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
BSD-style license. See DJUTILS License.

Author:
Alexander Verbraeck, Peter Knoppers

  • Constructor Summary

    Constructors
    Constructor
    Description
    Transform3d()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    equals(Object obj)
    double[]
    getMat()
    Get a safe copy of the affine transformation matrix.
    int
    hashCode()
    protected static double[]
    mulMatMat(double[] m1, double[] m2)
    Multiply a 4x4 matrix (stored as a 16-value array by row) with another 4x4-matrix.
    protected static double[]
    mulMatVec(double[] m, double[] v)
    Multiply a 4x4 matrix (stored as a 16-value array by row) with a 4-value vector.
    protected static double[]
    mulMatVec3(double[] m, double[] v)
    Multiply a 4x4 matrix (stored as a 16-value array by row) with a 3-value vector and a 1 for the 4th value.
    Transform3d
    reflectX()
    The reflection of the x-coordinate, by mirroring it in the yz-plane (the plane with x=0).
    Transform3d
    reflectY()
    The reflection of the y-coordinate, by mirroring it in the xz-plane (the plane with y=0).
    Transform3d
    reflectZ()
    The reflection of the z-coordinate, by mirroring it in the xy-plane (the plane with z=0).
    Transform3d
    rotX(double angle)
    The Euler rotation around the x-axis with an angle in radians.
    Transform3d
    rotY(double angle)
    The Euler rotation around the y-axis with an angle in radians.
    Transform3d
    rotZ(double angle)
    The Euler rotation around the z-axis with an angle in radians.
    Transform3d
    scale(double sx, double sy, double sz)
    Scale all coordinates with a factor for x, y, and z.
    Transform3d
    shearXY(double sx, double sy)
    The xy-shear leaves the xy-coordinate plane for z=0 untouched.
    Transform3d
    shearXZ(double sx, double sz)
    The xz-shear leaves the xz-coordinate plain for y=0 untouched.
    Transform3d
    shearYZ(double sy, double sz)
    The yz-shear leaves the yz-coordinate plain for x=0 untouched.
    String
    toString()
    double[]
    transform(double[] xyz)
    Apply the stored transform on the xyz-vector and return the transformed vector.
    Iterator<Point3d>
    transform(Iterator<Point3d> pointIterator)
    Apply the stored transform on the provided point and return a point with the transformed coordinate.
    Bounds3d
    transform(Bounds3d boundingBox)
    Apply the stored transform on the provided Bounds3d and return a new Bounds3d with the bounds of the transformed coordinates.
    Point3d
    transform(Point3d point)
    Apply the stored transform on the provided point and return a point with the transformed coordinate.
    Transform3d
    translate(double tx, double ty, double tz)
    Transform coordinates by a vector (tx, ty, tz).
    Transform3d
    translate(Point3d point)
    Translate coordinates by a the x, y, and z values contained in a Point.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Constructor Details

    • Transform3d

      public Transform3d()

  • Method Details

    • mulMatVec

      protected static double[] mulMatVec(double[] m, double[] v)
      Multiply a 4x4 matrix (stored as a 16-value array by row) with a 4-value vector.
      Parameters:
      m - double[]; the matrix
      v - double[]; the vector
      Returns:
      double[4]; the result of m x v

    • mulMatVec3

      protected static double[] mulMatVec3(double[] m, double[] v)
      Multiply a 4x4 matrix (stored as a 16-value array by row) with a 3-value vector and a 1 for the 4th value.
      Parameters:
      m - double[]; the matrix
      v - double[]; the vector
      Returns:
      double[3]; the result of m x (v1, v2, v3, 1), with the last value left out

    • mulMatMat

      protected static double[] mulMatMat(double[] m1, double[] m2)
      Multiply a 4x4 matrix (stored as a 16-value array by row) with another 4x4-matrix.
      Parameters:
      m1 - double[]; the first matrix
      m2 - double[]; the second matrix
      Returns:
      double[16]; the result of m1 x m2

    • getMat

      public double[] getMat()
      Get a safe copy of the affine transformation matrix.
      Returns:
      double[]; a safe copy of the affine transformation matrix

    • translate

      public Transform3d translate(double tx, double ty, double tz)
      Transform coordinates by a vector (tx, ty, tz). Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      tx - double; the translation value for the x-coordinates
      ty - double; the translation value for the y-coordinates
      tz - double; the translation value for the z-coordinates
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • translate

      public Transform3d translate(Point3d point)
      Translate coordinates by a the x, y, and z values contained in a Point. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      point - Point3d; the point containing the x, y, and z translation values
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • scale

      public Transform3d scale(double sx, double sy, double sz)
      Scale all coordinates with a factor for x, y, and z. A scale factor of 1 leaves the coordinate unchanged. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      sx - double; the scale factor for the x-coordinates
      sy - double; the scale factor for the y-coordinates
      sz - double; the scale factor for the z-coordinates
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • rotX

      public Transform3d rotX(double angle)
      The Euler rotation around the x-axis with an angle in radians. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      angle - double; the angle to rotate the coordinates with with around the x-axis
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • rotY

      public Transform3d rotY(double angle)
      The Euler rotation around the y-axis with an angle in radians. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      angle - double; the angle to rotate the coordinates with with around the y-axis
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • rotZ

      public Transform3d rotZ(double angle)
      The Euler rotation around the z-axis with an angle in radians. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      angle - double; the angle to rotate the coordinates with with around the z-axis
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • shearXY

      public Transform3d shearXY(double sx, double sy)
      The xy-shear leaves the xy-coordinate plane for z=0 untouched. Coordinates on z=1 are translated by a vector (sx, sy, 0). Coordinates for points with other z-values are translated by a vector (z.sx, z.sy, 0), where z is the z-coordinate of the point. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      sx - double; the shear factor in the x-direction for z=1
      sy - double; the shear factor in the y-direction for z=1
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • shearYZ

      public Transform3d shearYZ(double sy, double sz)
      The yz-shear leaves the yz-coordinate plain for x=0 untouched. Coordinates on x=1 are translated by a vector (0, sy, sz). Coordinates for points with other x-values are translated by a vector (0, x.sy, x.sz), where x is the x-coordinate of the point. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      sy - double; the shear factor in the y-direction for x=1
      sz - double; the shear factor in the z-direction for x=1
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • shearXZ

      public Transform3d shearXZ(double sx, double sz)
      The xz-shear leaves the xz-coordinate plain for y=0 untouched. Coordinates on y=1 are translated by a vector (sx, 0, sz). Coordinates for points with other y-values are translated by a vector (y.sx, 0, y.sz), where y is the y-coordinate of the point. Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Parameters:
      sx - double; the shear factor in the y-direction for y=1
      sz - double; the shear factor in the z-direction for y=1
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • reflectX

      public Transform3d reflectX()
      The reflection of the x-coordinate, by mirroring it in the yz-plane (the plane with x=0). Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • reflectY

      public Transform3d reflectY()
      The reflection of the y-coordinate, by mirroring it in the xz-plane (the plane with y=0). Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • reflectZ

      public Transform3d reflectZ()
      The reflection of the z-coordinate, by mirroring it in the xy-plane (the plane with z=0). Note that to carry out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      Returns:
      Transform3d; the new transformation matrix after applying this transform

    • transform

      public double[] transform(double[] xyz)
      Apply the stored transform on the xyz-vector and return the transformed vector. For speed reasons, no checks on correct size of the vector is done.
      Parameters:
      xyz - double[]; double[3] the provided vector
      Returns:
      double[3]; the transformed vector

    • transform

      public Point3d transform(Point3d point)
      Apply the stored transform on the provided point and return a point with the transformed coordinate.
      Parameters:
      point - Point3d; the point to be transformed
      Returns:
      Point3d; a point with the transformed coordinates

    • transform

      public Iterator<Point3d> transform(Iterator<Point3d> pointIterator)
      Apply the stored transform on the provided point and return a point with the transformed coordinate.
      Parameters:
      pointIterator - Iterator<Point3d>; generates the points to be transformed
      Returns:
      Iterator<Point3d>; an iterator that will generator all transformed points

    • transform

      public Bounds3d transform(Bounds3d boundingBox)
      Apply the stored transform on the provided Bounds3d and return a new Bounds3d with the bounds of the transformed coordinates. All 8 corner points have to be transformed, since we do not know which of the 8 points will result in the lowest and highest x, y, and z coordinates.
      Parameters:
      boundingBox - Bounds3d; the bounds to be transformed
      Returns:
      Bounds3d; the new bounds based on the transformed coordinates

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object

    • toString

      public String toString()
      Overrides:
      toString in class Object