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OpenDepthMap/libodm/dist/LeapMath.h

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/******************************************************************************\
* Copyright (C) 2012-2013 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 *
* between Leap Motion and you, your company or other organization. *
\******************************************************************************/
#if !defined(__LeapMath_h__)
#define __LeapMath_h__
#include <cmath>
#include <iostream>
#include <sstream>
#include <float.h>
#include <algorithm>
namespace Leap {
/**
* The constant pi as a single precision floating point number.
* @since 1.0
*/
static const float PI = 3.1415926536f;
/**
* The constant ratio to convert an angle measure from degrees to radians.
* Multiply a value in degrees by this constant to convert to radians.
* @since 1.0
*/
static const float DEG_TO_RAD = 0.0174532925f;
/**
* The constant ratio to convert an angle measure from radians to degrees.
* Multiply a value in radians by this constant to convert to degrees.
* @since 1.0
*/
static const float RAD_TO_DEG = 57.295779513f;
/**
* The difference between 1 and the least value greater than 1 that is
* representable as a float.
* @since 2.0
*/
static const float EPSILON = 1.192092896e-07f;
/**
* The Vector struct represents a three-component mathematical vector or point
* such as a direction or position in three-dimensional space.
*
* The Leap Motion software employs a right-handed Cartesian coordinate system.
* Values given are in units of real-world millimeters. The origin is centered
* at the center of the Leap Motion Controller. The x- and z-axes lie in the horizontal
* plane, with the x-axis running parallel to the long edge of the device.
* The y-axis is vertical, with positive values increasing upwards (in contrast
* to the downward orientation of most computer graphics coordinate systems).
* The z-axis has positive values increasing away from the computer screen.
*
* \image html images/Leap_Axes.png
* @since 1.0
*/
struct Vector {
/**
* Creates a new Vector with all components set to zero.
* @since 1.0
*/
Vector() :
x(0), y(0), z(0) {}
/**
* Creates a new Vector with the specified component values.
*
* \include Vector_Constructor_1.txt
* @since 1.0
*/
Vector(float _x, float _y, float _z) :
x(_x), y(_y), z(_z) {}
/**
* Copies the specified Vector.
*
* \include Vector_Constructor_2.txt
* @since 1.0
*/
Vector(const Vector& vector) :
x(vector.x), y(vector.y), z(vector.z) {}
/**
* The zero vector: (0, 0, 0)
*
* \include Vector_Zero.txt
* @since 1.0
*/
static const Vector& zero() {
static Vector s_zero(0, 0, 0);
return s_zero;
}
/**
* The x-axis unit vector: (1, 0, 0)
*
* \include Vector_XAxis.txt
* @since 1.0
*/
static const Vector& xAxis() {
static Vector s_xAxis(1, 0, 0);
return s_xAxis;
}
/**
* The y-axis unit vector: (0, 1, 0)
*
* \include Vector_YAxis.txt
* @since 1.0
*/
static const Vector& yAxis() {
static Vector s_yAxis(0, 1, 0);
return s_yAxis;
}
/**
* The z-axis unit vector: (0, 0, 1)
*
* \include Vector_ZAxis.txt
* @since 1.0
*/
static const Vector& zAxis() {
static Vector s_zAxis(0, 0, 1);
return s_zAxis;
}
/**
* The unit vector pointing left along the negative x-axis: (-1, 0, 0)
*
* \include Vector_Left.txt
* @since 1.0
*/
static const Vector& left() {
static Vector s_left(-1, 0, 0);
return s_left;
}
/**
* The unit vector pointing right along the positive x-axis: (1, 0, 0)
*
* \include Vector_Right.txt
* @since 1.0
*/
static const Vector& right() {
return xAxis();
}
/**
* The unit vector pointing down along the negative y-axis: (0, -1, 0)
*
* \include Vector_Down.txt
* @since 1.0
*/
static const Vector& down() {
static Vector s_down(0, -1, 0);
return s_down;
}
/**
* The unit vector pointing up along the positive y-axis: (0, 1, 0)
*
* \include Vector_Up.txt
* @since 1.0
*/
static const Vector& up() {
return yAxis();
}
/**
* The unit vector pointing forward along the negative z-axis: (0, 0, -1)
*
* \include Vector_Forward.txt
* @since 1.0
*/
static const Vector& forward() {
static Vector s_forward(0, 0, -1);
return s_forward;
}
/**
* The unit vector pointing backward along the positive z-axis: (0, 0, 1)
*
* \include Vector_Backward.txt
* @since 1.0
*/
static const Vector& backward() {
return zAxis();
}
/**
* The magnitude, or length, of this vector.
*
* The magnitude is the L2 norm, or Euclidean distance between the origin and
* the point represented by the (x, y, z) components of this Vector object.
*
* \include Vector_Magnitude.txt
*
* @returns The length of this vector.
* @since 1.0
*/
float magnitude() const {
return std::sqrt(x*x + y*y + z*z);
}
/**
* The square of the magnitude, or length, of this vector.
*
* \include Vector_Magnitude_Squared.txt
*
* @returns The square of the length of this vector.
* @since 1.0
*/
float magnitudeSquared() const {
return x*x + y*y + z*z;
}
/**
* The distance between the point represented by this Vector
* object and a point represented by the specified Vector object.
*
* \include Vector_DistanceTo.txt
*
* @param other A Vector object.
* @returns The distance from this point to the specified point.
* @since 1.0
*/
float distanceTo(const Vector& other) const {
return std::sqrt((x - other.x)*(x - other.x) +
(y - other.y)*(y - other.y) +
(z - other.z)*(z - other.z));
}
/**
* The angle between this vector and the specified vector in radians.
*
* The angle is measured in the plane formed by the two vectors. The
* angle returned is always the smaller of the two conjugate angles.
* Thus <tt>A.angleTo(B) == B.angleTo(A)</tt> and is always a positive
* value less than or equal to pi radians (180 degrees).
*
* If either vector has zero length, then this function returns zero.
*
* \image html images/Math_AngleTo.png
*
* \include Vector_AngleTo.txt
*
* @param other A Vector object.
* @returns The angle between this vector and the specified vector in radians.
* @since 1.0
*/
float angleTo(const Vector& other) const {
float denom = this->magnitudeSquared() * other.magnitudeSquared();
if (denom <= EPSILON) {
return 0.0f;
}
float val = this->dot(other) / std::sqrt(denom);
if (val >= 1.0f) {
return 0.0f;
} else if (val <= -1.0f) {
return PI;
}
return std::acos(val);
}
/**
* The pitch angle in radians.
*
* Pitch is the angle between the negative z-axis and the projection of
* the vector onto the y-z plane. In other words, pitch represents rotation
* around the x-axis.
* If the vector points upward, the returned angle is between 0 and pi radians
* (180 degrees); if it points downward, the angle is between 0 and -pi radians.
*
* \image html images/Math_Pitch_Angle.png
*
* \include Vector_Pitch.txt
*
* @returns The angle of this vector above or below the horizon (x-z plane).
* @since 1.0
*/
float pitch() const {
return std::atan2(y, -z);
}
/**
* The yaw angle in radians.
*
* Yaw is the angle between the negative z-axis and the projection of
* the vector onto the x-z plane. In other words, yaw represents rotation
* around the y-axis. If the vector points to the right of the negative z-axis,
* then the returned angle is between 0 and pi radians (180 degrees);
* if it points to the left, the angle is between 0 and -pi radians.
*
* \image html images/Math_Yaw_Angle.png
*
* \include Vector_Yaw.txt
*
* @returns The angle of this vector to the right or left of the negative z-axis.
* @since 1.0
*/
float yaw() const {
return std::atan2(x, -z);
}
/**
* The roll angle in radians.
*
* Roll is the angle between the y-axis and the projection of
* the vector onto the x-y plane. In other words, roll represents rotation
* around the z-axis. If the vector points to the left of the y-axis,
* then the returned angle is between 0 and pi radians (180 degrees);
* if it points to the right, the angle is between 0 and -pi radians.
*
* \image html images/Math_Roll_Angle.png
*
* Use this function to get roll angle of the plane to which this vector is a
* normal. For example, if this vector represents the normal to the palm,
* then this function returns the tilt or roll of the palm plane compared
* to the horizontal (x-z) plane.
*
* \include Vector_Roll.txt
*
* @returns The angle of this vector to the right or left of the y-axis.
* @since 1.0
*/
float roll() const {
return std::atan2(x, -y);
}
/**
* The dot product of this vector with another vector.
*
* The dot product is the magnitude of the projection of this vector
* onto the specified vector.
*
* \image html images/Math_Dot.png
*
* \include Vector_Dot.txt
*
* @param other A Vector object.
* @returns The dot product of this vector and the specified vector.
* @since 1.0
*/
float dot(const Vector& other) const {
return (x * other.x) + (y * other.y) + (z * other.z);
}
/**
* The cross product of this vector and the specified vector.
*
* The cross product is a vector orthogonal to both original vectors.
* It has a magnitude equal to the area of a parallelogram having the
* two vectors as sides. The direction of the returned vector is
* determined by the right-hand rule. Thus <tt>A.cross(B) == -B.cross(A).</tt>
*
* \image html images/Math_Cross.png
*
* \include Vector_Cross.txt
*
* @param other A Vector object.
* @returns The cross product of this vector and the specified vector.
* @since 1.0
*/
Vector cross(const Vector& other) const {
return Vector((y * other.z) - (z * other.y),
(z * other.x) - (x * other.z),
(x * other.y) - (y * other.x));
}
/**
* A normalized copy of this vector.
*
* A normalized vector has the same direction as the original vector,
* but with a length of one.
*
* \include Vector_Normalized.txt
*
* @returns A Vector object with a length of one, pointing in the same
* direction as this Vector object.
* @since 1.0
*/
Vector normalized() const {
float denom = this->magnitudeSquared();
if (denom <= EPSILON) {
return Vector::zero();
}
denom = 1.0f / std::sqrt(denom);
return Vector(x * denom, y * denom, z * denom);
}
/**
* A copy of this vector pointing in the opposite direction.
*
* \include Vector_Negate.txt
*
* @returns A Vector object with all components negated.
* @since 1.0
*/
Vector operator-() const {
return Vector(-x, -y, -z);
}
/**
* Add vectors component-wise.
*
* \include Vector_Plus.txt
* @since 1.0
*/
Vector operator+(const Vector& other) const {
return Vector(x + other.x, y + other.y, z + other.z);
}
/**
* Subtract vectors component-wise.
*
* \include Vector_Minus.txt
* @since 1.0
*/
Vector operator-(const Vector& other) const {
return Vector(x - other.x, y - other.y, z - other.z);
}
/**
* Multiply vector by a scalar.
*
* \include Vector_Times.txt
* @since 1.0
*/
Vector operator*(float scalar) const {
return Vector(x * scalar, y * scalar, z * scalar);
}
/**
* Divide vector by a scalar.
*
* \include Vector_Divide.txt
* @since 1.0
*/
Vector operator/(float scalar) const {
return Vector(x / scalar, y / scalar, z / scalar);
}
#if !defined(SWIG)
/**
* Multiply vector by a scalar on the left-hand side (C++ only).
*
* \include Vector_Left_Times.txt
* @since 1.0
*/
friend Vector operator*(float scalar, const Vector& vector) {
return Vector(vector.x * scalar, vector.y * scalar, vector.z * scalar);
}
#endif
/**
* Add vectors component-wise and assign the sum.
* @since 1.0
*/
Vector& operator+=(const Vector& other) {
x += other.x;
y += other.y;
z += other.z;
return *this;
}
/**
* Subtract vectors component-wise and assign the difference.
* @since 1.0
*/
Vector& operator-=(const Vector& other) {
x -= other.x;
y -= other.y;
z -= other.z;
return *this;
}
/**
* Multiply vector by a scalar and assign the product.
* @since 1.0
*/
Vector& operator*=(float scalar) {
x *= scalar;
y *= scalar;
z *= scalar;
return *this;
}
/**
* Divide vector by a scalar and assign the quotient.
* @since 1.0
*/
Vector& operator/=(float scalar) {
x /= scalar;
y /= scalar;
z /= scalar;
return *this;
}
/**
* Returns a string containing this vector in a human readable format: (x, y, z).
* @since 1.0
*/
std::string toString() const {
std::stringstream result;
result << "(" << x << ", " << y << ", " << z << ")";
return result.str();
}
/**
* Writes the vector to the output stream using a human readable format: (x, y, z).
* @since 1.0
*/
friend std::ostream& operator<<(std::ostream& out, const Vector& vector) {
return out << vector.toString();
}
/**
* Compare Vector equality component-wise.
*
* \include Vector_Equals.txt
* @since 1.0
*/
bool operator==(const Vector& other) const {
return x == other.x && y == other.y && z == other.z;
}
/**
* Compare Vector inequality component-wise.
*
* \include Vector_NotEqual.txt
* @since 1.0
*/
bool operator!=(const Vector& other) const {
return x != other.x || y != other.y || z != other.z;
}
/**
* Returns true if all of the vector's components are finite. If any
* component is NaN or infinite, then this returns false.
*
* \include Vector_IsValid.txt
* @since 1.0
*/
bool isValid() const {
return (x <= FLT_MAX && x >= -FLT_MAX) &&
(y <= FLT_MAX && y >= -FLT_MAX) &&
(z <= FLT_MAX && z >= -FLT_MAX);
}
/**
* Index vector components numerically.
* Index 0 is x, index 1 is y, and index 2 is z.
* @returns The x, y, or z component of this Vector, if the specified index
* value is at least 0 and at most 2; otherwise, returns zero.
*
* \include Vector_Index.txt
* @since 1.0
*/
float operator[](unsigned int index) const {
return index < 3 ? (&x)[index] : 0.0f;
}
/**
* Cast the vector to a float array.
*
* \include Vector_ToFloatPointer.txt
* @since 1.0
*/
const float* toFloatPointer() const {
return &x; /* Note: Assumes x, y, z are aligned in memory. */
}
/**
* Convert a Leap::Vector to another 3-component Vector type.
*
* The specified type must define a constructor that takes the x, y, and z
* components as separate parameters.
* @since 1.0
*/
template<typename Vector3Type>
const Vector3Type toVector3() const {
return Vector3Type(x, y, z);
}
/**
* Convert a Leap::Vector to another 4-component Vector type.
*
* The specified type must define a constructor that takes the x, y, z, and w
* components as separate parameters. (The homogeneous coordinate, w, is set
* to zero by default, but you should typically set it to one for vectors
* representing a position.)
* @since 1.0
*/
template<typename Vector4Type>
const Vector4Type toVector4(float w=0.0f) const {
return Vector4Type(x, y, z, w);
}
/**
* The horizontal component.
* @since 1.0
*/
float x;
/**
* The vertical component.
* @since 1.0
*/
float y;
/**
* The depth component.
* @since 1.0
*/
float z;
};
/**
* The FloatArray struct is used to allow the returning of native float arrays
* without requiring dynamic memory allocation. It represents a matrix
* with a size up to 4x4.
* @since 1.0
*/
struct FloatArray {
/**
* Access the elements of the float array exactly like a native array.
* @since 1.0
*/
float& operator[] (unsigned int index) {
return m_array[index];
}
/**
* Use the Float Array anywhere a float pointer can be used.
* @since 1.0
*/
operator float* () {
return m_array;
}
/**
* Use the Float Array anywhere a const float pointer can be used.
* @since 1.0
*/
operator const float* () const {
return m_array;
}
/**
* An array containing up to 16 entries of the matrix.
* @since 1.0
*/
float m_array[16];
};
/**
* 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
*/
struct Matrix
{
/**
* Constructs an identity transformation matrix.
*
* \include Matrix_Matrix.txt
*
* @since 1.0
*/
Matrix() :
xBasis(1, 0, 0),
yBasis(0, 1, 0),
zBasis(0, 0, 1),
origin(0, 0, 0) {
}
/**
* Constructs a copy of the specified Matrix object.
*
* \include Matrix_Matrix_copy.txt
*
* @since 1.0
*/
Matrix(const Matrix& other) :
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
*/
Matrix(const Vector& _xBasis, const Vector& _yBasis, const Vector& _zBasis) :
xBasis(_xBasis),
yBasis(_yBasis),
zBasis(_zBasis),
origin(0, 0, 0) {
}
/**
* 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
*/
Matrix(const Vector& _xBasis, const Vector& _yBasis, const Vector& _zBasis, const Vector& _origin) :
xBasis(_xBasis),
yBasis(_yBasis),
zBasis(_zBasis),
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
*/
Matrix(const Vector& axis, float angleRadians) :
origin(0, 0, 0) {
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
*/
Matrix(const Vector& axis, float angleRadians, const Vector& translation)
: origin(translation) {
setRotation(axis, angleRadians);
}
/**
* Returns the identity matrix specifying no translation, rotation, and scale.
*
* \include Matrix_identity.txt
*
* @returns The identity matrix.
* @since 1.0
*/
static const Matrix& identity() {
static Matrix s_identity;
return s_identity;
}
/**
* 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
*/
void setRotation(const Vector& axis, float angleRadians) {
const Vector n = axis.normalized();
const float s = std::sin(angleRadians);
const float c = std::cos(angleRadians);
const float C = (1-c);
xBasis = Vector(n[0]*n[0]*C + c, n[0]*n[1]*C - n[2]*s, n[0]*n[2]*C + n[1]*s);
yBasis = Vector(n[1]*n[0]*C + n[2]*s, n[1]*n[1]*C + c, n[1]*n[2]*C - n[0]*s);
zBasis = Vector(n[2]*n[0]*C - n[1]*s, n[2]*n[1]*C + n[0]*s, n[2]*n[2]*C + c );
}
/**
* 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 in The Vector to transform.
* @returns A new Vector representing the transformed original.
* @since 1.0
*/
Vector transformPoint(const Vector& in) const {
return xBasis*in.x + yBasis*in.y + zBasis*in.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
*/
Vector transformDirection(const Vector& in) const {
return xBasis*in.x + yBasis*in.y + zBasis*in.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
*/
Matrix rigidInverse() const {
Matrix rotInverse = Matrix(Vector(xBasis[0], yBasis[0], zBasis[0]),
Vector(xBasis[1], yBasis[1], zBasis[1]),
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
*/
Matrix operator*(const Matrix& other) const {
return Matrix(transformDirection(other.xBasis),
transformDirection(other.yBasis),
transformDirection(other.zBasis),
transformPoint(other.origin));
}
/**
* Multiply transform matrices and assign the product.
*
* \include Matrix_operator_times_equal.txt
*
* @since 1.0
*/
Matrix& operator*=(const Matrix& other) {
return (*this) = (*this) * other;
}
/**
* Compare Matrix equality component-wise.
*
* \include Matrix_operator_equals.txt
*
* @since 1.0
*/
bool operator==(const Matrix& other) const {
return xBasis == other.xBasis &&
yBasis == other.yBasis &&
zBasis == other.zBasis &&
origin == other.origin;
}
/**
* Compare Matrix inequality component-wise.
*
* \include Matrix_operator_not_equals.txt
*
* @since 1.0
*/
bool operator!=(const Matrix& other) const {
return xBasis != other.xBasis ||
yBasis != other.yBasis ||
zBasis != other.zBasis ||
origin != other.origin;
}
/**
* Convert a Leap::Matrix object to another 3x3 matrix type.
*
* The new type must define a constructor function that takes each matrix
* element as a parameter in row-major order.
*
* Translation factors are discarded.
* @since 1.0
*/
template<typename Matrix3x3Type>
const Matrix3x3Type toMatrix3x3() const {
return Matrix3x3Type(xBasis.x, xBasis.y, xBasis.z,
yBasis.x, yBasis.y, yBasis.z,
zBasis.x, zBasis.y, zBasis.z);
}
/**
* Convert a Leap::Matrix object to another 4x4 matrix type.
*
* The new type must define a constructor function that takes each matrix
* element as a parameter in row-major order.
* @since 1.0
*/
template<typename Matrix4x4Type>
const Matrix4x4Type toMatrix4x4() const {
return Matrix4x4Type(xBasis.x, xBasis.y, xBasis.z, 0.0f,
yBasis.x, yBasis.y, yBasis.z, 0.0f,
zBasis.x, zBasis.y, zBasis.z, 0.0f,
origin.x, origin.y, origin.z, 1.0f);
}
/**
* Writes the 3x3 Matrix object to a 9 element row-major float or
* double array.
*
* Translation factors are discarded.
*
* Returns a pointer to the same data.
* @since 1.0
*/
template<typename T>
T* toArray3x3(T* output) const {
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 a 3x3 Matrix object to a 9 element row-major float array.
*
* Translation factors are discarded.
*
* \include Matrix_toArray3x3.txt
*
* Returns a FloatArray struct to avoid dynamic memory allocation.
* @since 1.0
*/
FloatArray toArray3x3() const {
FloatArray output;
toArray3x3((float*)output);
return output;
}
/**
* Writes the 4x4 Matrix object to a 16 element row-major float
* or double array.
*
* Returns a pointer to the same data.
* @since 1.0
*/
template<typename T>
T* toArray4x4(T* output) const {
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 a 4x4 Matrix object to a 16 element row-major float array.
*
* \include Matrix_toArray4x4.txt
*
* Returns a FloatArray struct to avoid dynamic memory allocation.
* @since 1.0
*/
FloatArray toArray4x4() const {
FloatArray output;
toArray4x4((float*)output);
return output;
}
/**
* Write the matrix to a string in a human readable format.
* @since 1.0
*/
std::string toString() const {
std::stringstream result;
result << "xBasis:" << xBasis.toString() << " yBasis:" << yBasis.toString()
<< " zBasis:" << zBasis.toString() << " origin:" << origin.toString();
return result.str();
}
/**
* Write the matrix to an output stream in a human readable format.
*
* \include Matrix_operator_stream.txt
*
* @since 1.0
*/
friend std::ostream& operator<<(std::ostream& out, const Matrix& matrix) {
return out << matrix.toString();
}
/**
* The basis vector for the x-axis.
*
* \include Matrix_xBasis.txt
*
* @since 1.0
*/
Vector xBasis;
/**
* The basis vector for the y-axis.
*
* \include Matrix_yBasis.txt
*
* @since 1.0
*/
Vector yBasis;
/**
* The basis vector for the z-axis.
*
* \include Matrix_zBasis.txt
*
* @since 1.0
*/
Vector zBasis;
/**
* The translation factors for all three axes.
*
* \include Matrix_origin.txt
*
* @since 1.0
*/
Vector origin;
};
}; // namespace Leap
#endif // __LeapMath_h__
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