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* Copyright (C) 2012-2016 Leap Motion, Inc. All rights reserved. *
* Leap Motion proprietary and confidential. Not for distribution. *
* Use subject to the terms of the Leap Motion SDK Agreement available at *
* https://developer.leapmotion.com/sdk_agreement, or another agreement *
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\******************************************************************************/
namespace Leap
{
using System;
/**
* The Matrix struct represents a transformation matrix.
*
* To use this struct to transform a Vector, construct a matrix containing the
* desired transformation and then use the Matrix::transformPoint() or
* Matrix::transformDirection() functions to apply the transform.
*
* Transforms can be combined by multiplying two or more transform matrices using
* the * operator.
* @since 1.0
*/
public struct Matrix
{
/** Multiply two matrices. */
public static Matrix operator *(Matrix m1, Matrix m2)
{
return m1._operator_mul(m2);
}
/** Copy this matrix to the specified array of 9 float values in row-major order. */
public float[] ToArray3x3(float[] output)
{
output[0] = xBasis.x;
output[1] = xBasis.y;
output[2] = xBasis.z;
output[3] = yBasis.x;
output[4] = yBasis.y;
output[5] = yBasis.z;
output[6] = zBasis.x;
output[7] = zBasis.y;
output[8] = zBasis.z;
return output;
}
/** Copy this matrix to the specified array containing 9 double values in row-major order. */
public double[] ToArray3x3(double[] output)
{
output[0] = xBasis.x;
output[1] = xBasis.y;
output[2] = xBasis.z;
output[3] = yBasis.x;
output[4] = yBasis.y;
output[5] = yBasis.z;
output[6] = zBasis.x;
output[7] = zBasis.y;
output[8] = zBasis.z;
return output;
}
/** Convert this matrix to an array containing 9 float values in row-major order. */
public float[] ToArray3x3()
{
return ToArray3x3(new float[9]);
}
/** Copy this matrix to the specified array of 16 float values in row-major order. */
public float[] ToArray4x4(float[] output)
{
output[0] = xBasis.x;
output[1] = xBasis.y;
output[2] = xBasis.z;
output[3] = 0.0f;
output[4] = yBasis.x;
output[5] = yBasis.y;
output[6] = yBasis.z;
output[7] = 0.0f;
output[8] = zBasis.x;
output[9] = zBasis.y;
output[10] = zBasis.z;
output[11] = 0.0f;
output[12] = origin.x;
output[13] = origin.y;
output[14] = origin.z;
output[15] = 1.0f;
return output;
}
/** Copy this matrix to the specified array of 16 double values in row-major order. */
public double[] ToArray4x4(double[] output)
{
output[0] = xBasis.x;
output[1] = xBasis.y;
output[2] = xBasis.z;
output[3] = 0.0f;
output[4] = yBasis.x;
output[5] = yBasis.y;
output[6] = yBasis.z;
output[7] = 0.0f;
output[8] = zBasis.x;
output[9] = zBasis.y;
output[10] = zBasis.z;
output[11] = 0.0f;
output[12] = origin.x;
output[13] = origin.y;
output[14] = origin.z;
output[15] = 1.0f;
return output;
}
/** Convert this matrix to an array containing 16 float values in row-major order. */
public float[] ToArray4x4()
{
return ToArray4x4(new float[16]);
}
/**
* Constructs a copy of the specified Matrix object.
*
* \include Matrix_Matrix_copy.txt
*
* @since 1.0
*/
public Matrix(Matrix other):
this()
{
xBasis = other.xBasis;
yBasis = other.yBasis;
zBasis = other.zBasis;
origin = other.origin;
}
/**
* Constructs a transformation matrix from the specified basis vectors.
*
* \include Matrix_Matrix_basis.txt
*
* @param xBasis A Vector specifying rotation and scale factors for the x-axis.
* @param yBasis A Vector specifying rotation and scale factors for the y-axis.
* @param zBasis A Vector specifying rotation and scale factors for the z-axis.
* @since 1.0
*/
public Matrix(Vector xBasis, Vector yBasis, Vector zBasis) :
this()
{
this.xBasis = xBasis;
this.yBasis = yBasis;
this.zBasis = zBasis;
this.origin = Vector.Zero;
}
/**
* Constructs a transformation matrix from the specified basis and translation vectors.
*
* \include Matrix_Matrix_basis_origin.txt
*
* @param xBasis A Vector specifying rotation and scale factors for the x-axis.
* @param yBasis A Vector specifying rotation and scale factors for the y-axis.
* @param zBasis A Vector specifying rotation and scale factors for the z-axis.
* @param origin A Vector specifying translation factors on all three axes.
* @since 1.0
*/
public Matrix(Vector xBasis, Vector yBasis, Vector zBasis, Vector origin) :
this()
{
this.xBasis = xBasis;
this.yBasis = yBasis;
this.zBasis = zBasis;
this.origin = origin;
}
/**
* Constructs a transformation matrix specifying a rotation around the specified vector.
*
* \include Matrix_Matrix_rotation.txt
*
* @param axis A Vector specifying the axis of rotation.
* @param angleRadians The amount of rotation in radians.
* @since 1.0
*/
public Matrix(Vector axis, float angleRadians) :
this()
{
xBasis = Vector.XAxis;
yBasis = Vector.YAxis;
zBasis = Vector.ZAxis;
origin = Vector.Zero;
this.SetRotation(axis, angleRadians);
}
/**
* Constructs a transformation matrix specifying a rotation around the specified vector
* and a translation by the specified vector.
*
* \include Matrix_Matrix_rotation_translation.txt
*
* @param axis A Vector specifying the axis of rotation.
* @param angleRadians The angle of rotation in radians.
* @param translation A Vector representing the translation part of the transform.
* @since 1.0
*/
public Matrix(Vector axis, float angleRadians, Vector translation) :
this()
{
xBasis = Vector.XAxis;
yBasis = Vector.YAxis;
zBasis = Vector.ZAxis;
origin = translation;
this.SetRotation(axis, angleRadians);
}
public Matrix(float m00,
float m01,
float m02,
float m10,
float m11,
float m12,
float m20,
float m21,
float m22) :
this()
{
xBasis = new Vector(m00, m01, m02);
yBasis = new Vector(m10, m11, m12);
zBasis = new Vector(m20, m21, m22);
origin = Vector.Zero;
}
public Matrix(float m00,
float m01,
float m02,
float m10,
float m11,
float m12,
float m20,
float m21,
float m22,
float m30,
float m31,
float m32) :
this()
{
xBasis = new Vector(m00, m01, m02);
yBasis = new Vector(m10, m11, m12);
zBasis = new Vector(m20, m21, m22);
origin = new Vector(m30, m31, m32);
}
/**
* Sets this transformation matrix to represent a rotation around the specified vector.
*
* \include Matrix_setRotation.txt
*
* This function erases any previous rotation and scale transforms applied
* to this matrix, but does not affect translation.
*
* @param axis A Vector specifying the axis of rotation.
* @param angleRadians The amount of rotation in radians.
* @since 1.0
*/
public void SetRotation(Vector axis, float angleRadians)
{
Vector n = axis.Normalized;
float s = (float)Math.Sin(angleRadians);
float c = (float)Math.Cos(angleRadians);
float C = (1 - c);
xBasis = new Vector(n[0] * n[0] * C + c, n[0] * n[1] * C - n[2] * s, n[0] * n[2] * C + n[1] * s);
yBasis = new Vector(n[1] * n[0] * C + n[2] * s, n[1] * n[1] * C + c, n[1] * n[2] * C - n[0] * s);
zBasis = new Vector(n[2] * n[0] * C - n[1] * s, n[2] * n[1] * C + n[0] * s, n[2] * n[2] * C + c);
}
//TODO functions for getting Axis and Angle from matrix
/**
* Transforms a vector with this matrix by transforming its rotation,
* scale, and translation.
*
* \include Matrix_transformPoint.txt
*
* Translation is applied after rotation and scale.
*
* @param point The Vector to transform.
* @returns A new Vector representing the transformed original.
* @since 1.0
*/
public Vector TransformPoint(Vector point)
{
return xBasis * point.x + yBasis * point.y + zBasis * point.z + origin;
}
/**
* Transforms a vector with this matrix by transforming its rotation and
* scale only.
*
* \include Matrix_transformDirection.txt
*
* @param in The Vector to transform.
* @returns A new Vector representing the transformed original.
* @since 1.0
*/
public Vector TransformDirection(Vector direction)
{
return xBasis * direction.x + yBasis * direction.y + zBasis * direction.z;
}
/**
* Performs a matrix inverse if the matrix consists entirely of rigid
* transformations (translations and rotations). If the matrix is not rigid,
* this operation will not represent an inverse.
*
* \include Matrix_rigidInverse.txt
*
* Note that all matrices that are directly returned by the API are rigid.
*
* @returns The rigid inverse of the matrix.
* @since 1.0
*/
public Matrix RigidInverse()
{
Matrix rotInverse = new Matrix(new Vector(xBasis[0], yBasis[0], zBasis[0]),
new Vector(xBasis[1], yBasis[1], zBasis[1]),
new Vector(xBasis[2], yBasis[2], zBasis[2]));
rotInverse.origin = rotInverse.TransformDirection(-origin);
return rotInverse;
}
/**
* Multiply transform matrices.
*
* Combines two transformations into a single equivalent transformation.
*
* \include Matrix_operator_times.txt
*
* @param other A Matrix to multiply on the right hand side.
* @returns A new Matrix representing the transformation equivalent to
* applying the other transformation followed by this transformation.
* @since 1.0
*/
private Matrix _operator_mul(Matrix other)
{
return new Matrix(TransformDirection(other.xBasis),
TransformDirection(other.yBasis),
TransformDirection(other.zBasis),
TransformPoint(other.origin));
}
/**
* Compare Matrix equality component-wise.
*
* \include Matrix_operator_equals.txt
*
* @since 1.0
*/
public bool Equals(Matrix other)
{
return xBasis == other.xBasis &&
yBasis == other.yBasis &&
zBasis == other.zBasis &&
origin == other.origin;
}
/**
* Write the matrix to a string in a human readable format.
* @since 1.0
*/
public override string ToString()
{
return string.Format("xBasis: {0} yBasis: {1} zBasis: {2} origin: {3}", xBasis, yBasis, zBasis, origin);
}
/**
* The basis vector for the x-axis.
*
* \include Matrix_xBasis.txt
*
* @since 1.0
*/
public Vector xBasis { get; set; }
/**
* The basis vector for the y-axis.
*
* \include Matrix_yBasis.txt
*
* @since 1.0
*/
public Vector yBasis { get; set; }
/**
* The basis vector for the z-axis.
*
* \include Matrix_zBasis.txt
*
* @since 1.0
*/
public Vector zBasis { get; set; }
/**
* The translation factors for all three axes.
*
* \include Matrix_origin.txt
*
* @since 1.0
*/
public Vector origin { get; set; }
/**
* Returns the identity matrix specifying no translation, rotation, and scale.
*
* \include Matrix_identity.txt
*
* @returns The identity matrix.
* @since 1.0
*/
public static readonly Matrix Identity = new Matrix(Vector.XAxis, Vector.YAxis, Vector.ZAxis, Vector.Zero);
}
}
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