georegression.geometry

Class GeometryMath_F64

java.lang.Object

georegression.geometry.GeometryMath_F64

public class GeometryMath_F64
extends java.lang.Object

Math operations that can be applied to geometric primitives.

Constructor Summary

Constructors

Constructor and Description
GeometryMath_F64()

Method Summary

Modifier and Type	Method and Description
static void	add(double a0, GeoTuple3D_F64 pt0, double a1, GeoTuple3D_F64 pt1, GeoTuple3D_F64 pt2) Adds two points together while scaling them. pt2 = a0 pt0 + a1 pt1
static void	add(GeoTuple3D_F64 a, GeoTuple3D_F64 b, GeoTuple3D_F64 c) Adds two points together. c = a + b
static <T extends GeoTuple3D_F64> T	addMult(T p0, org.ejml.data.DenseMatrix64F M, T p1, T ret) ret = p0 + M*p1
static org.ejml.data.DenseMatrix64F	addOuterProd(org.ejml.data.DenseMatrix64F A, double scalar, GeoTuple3D_F64 b, GeoTuple3D_F64 c, org.ejml.data.DenseMatrix64F ret) Adds the outer product of two vectors onto a matrix: ret = A + scalar*a*bT
static void	changeSign(GeoTuple3D_F64 t) Changes the sign of the vector: T = -T
static void	cross(double a_x, double a_y, double a_z, double b_x, double b_y, double b_z, GeoTuple3D_F64 c) Computes the cross product: c = a x b
static void	cross(GeoTuple2D_F64 a, GeoTuple2D_F64 b, GeoTuple3D_F64 c) Computes the cross product: c = a x b
static void	cross(GeoTuple2D_F64 a, GeoTuple3D_F64 b, GeoTuple3D_F64 c) Computes the cross product: c = a x b where 'a' is in homogeneous coordinates.
static void	cross(GeoTuple3D_F64 a, GeoTuple3D_F64 b, GeoTuple3D_F64 c) Computes the cross product: c = a x b
static org.ejml.data.DenseMatrix64F	crossMatrix(double x0, double x1, double x2, org.ejml.data.DenseMatrix64F ret) Creates a skew symmetric cross product matrix from the provided tuple.
static org.ejml.data.DenseMatrix64F	crossMatrix(GeoTuple3D_F64 v, org.ejml.data.DenseMatrix64F ret) Creates a skew symmetric cross product matrix from the provided tuple.
static double	dot(GeoTuple3D_F64 a, GeoTuple3D_F64 b) Dot product: ret = aTb
static double	innerProd(GeoTuple2D_F64 a, org.ejml.data.DenseMatrix64F M, GeoTuple2D_F64 b) Computes the inner matrix product: ret = a'*M*b where ret is a scalar number.
static double	innerProd(GeoTuple3D_F64 a, org.ejml.data.DenseMatrix64F M, GeoTuple3D_F64 b) ret = aT*M*b
static double	innerProdTranM(GeoTuple3D_F64 a, org.ejml.data.DenseMatrix64F M, GeoTuple3D_F64 b) Computes the inner matrix product: ret = xTATy
static void	mult(org.ejml.data.DenseMatrix64F M, GeoTuple2D_F64 pt, GeoTuple3D_F64 mod) mod = M*pt where pt has z=1 implicitly.
static <T extends GeoTuple2D_F64> T	mult(org.ejml.data.DenseMatrix64F M, GeoTuple3D_F64 pt, T mod) mod = M*pt where mod is a 2D point that has an implicit z=1.
static <T extends GeoTuple2D_F64> T	mult(org.ejml.data.DenseMatrix64F M, T pt, T mod) Computes mod = M*pt, where both pt and mod are in homogeneous coordinates with z assumed to be equal to 1, and M is a 3x3 matrix.
static <T extends GeoTuple3D_F64> T	mult(org.ejml.data.DenseMatrix64F M, T pt, T result) mod = M*pt
static org.ejml.data.DenseMatrix64F	multCrossA(GeoTuple2D_F64 A, org.ejml.data.DenseMatrix64F M, org.ejml.data.DenseMatrix64F result) Computes the following: result = cross(A)*M where M and result are 3x3 matrices, cross(A) is the cross product matrix of A.
static org.ejml.data.DenseMatrix64F	multCrossA(GeoTuple3D_F64 A, org.ejml.data.DenseMatrix64F M, org.ejml.data.DenseMatrix64F result) Computes the following: result = cross(A)*M where M and result are 3x3 matrices, cross(A) is the cross product matrix of A.
static <T extends GeoTuple2D_F64> T	multTran(org.ejml.data.DenseMatrix64F M, GeoTuple2D_F64 pt, T mod) mod = MT*pt where pt.z = 1 implicitly.
static <T extends GeoTuple3D_F64> T	multTran(org.ejml.data.DenseMatrix64F M, GeoTuple2D_F64 pt, T mod) mod = MT*pt where pt.z = 1 implicitly.
static <T extends GeoTuple3D_F64> T	multTran(org.ejml.data.DenseMatrix64F M, T pt, T mod) mod = MT*pt.
static org.ejml.data.DenseMatrix64F	outerProd(GeoTuple3D_F64 a, GeoTuple3D_F64 b, org.ejml.data.DenseMatrix64F ret) Computes the outer product of two vectors: O = a*bT
static void	rotate(double c, double s, GeoTuple2D_F64 pt, GeoTuple2D_F64 solution) Rotates a 2D point by the specified angle.
static void	rotate(double theta, GeoTuple2D_F64 pt, GeoTuple2D_F64 solution) Rotates a 2D point by the specified angle.
static void	scale(GeoTuple3D_F64 p, double v) Multiplies each element in the tuple by 'v'. pi=pi*v
static void	sub(GeoTuple3D_F64 a, GeoTuple3D_F64 b, GeoTuple3D_F64 c) Substracts two points from each other. c = a - b
static org.ejml.data.DenseMatrix64F	toMatrix(GeoTuple3D_F64 in, org.ejml.data.DenseMatrix64F out) Converts a GeoTuple3D_F64 into DenseMatrix64F
static void	toTuple3D(org.ejml.data.DenseMatrix64F in, GeoTuple3D_F64 out) Converts a DenseMatrix64F into GeoTuple3D_F64

Methods inherited from class java.lang.Object

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

Constructor Detail

GeometryMath_F64

public GeometryMath_F64()

Method Detail

crossMatrix

public static org.ejml.data.DenseMatrix64F crossMatrix(double x0,
                                                       double x1,
                                                       double x2,
                                                       org.ejml.data.DenseMatrix64F ret)

Creates a skew symmetric cross product matrix from the provided tuple.

Parameters:

x0 - Element 0.

x1 - Element 1.

x2 - Element 2.

ret - If not null the results are stored here, otherwise a new matrix is created.

Returns:

Skew symmetric cross product matrix.

crossMatrix

public static org.ejml.data.DenseMatrix64F crossMatrix(GeoTuple3D_F64 v,
                                                       org.ejml.data.DenseMatrix64F ret)

Creates a skew symmetric cross product matrix from the provided tuple.

Parameters:

v - Tuple. Not modified.

ret - If not null the results are stored here, otherwise a new matrix is created.

Returns:

Skew symmetric cross product matrix.

cross

public static void cross(GeoTuple3D_F64 a,
                         GeoTuple3D_F64 b,
                         GeoTuple3D_F64 c)

Computes the cross product:

c = a x b

Parameters:

a - Not modified.

b - Not modified.

c - Modified.

cross

public static void cross(double a_x,
                         double a_y,
                         double a_z,
                         double b_x,
                         double b_y,
                         double b_z,
                         GeoTuple3D_F64 c)

Computes the cross product:

c = a x b

Parameters:

a_x - x-coordinate of a

a_y - y-coordinate of a

a_z - z-coordinate of a

b_x - x-coordinate of b

b_y - y-coordinate of b

b_z - z-coordinate of b

c - Modified.

cross

public static void cross(GeoTuple2D_F64 a,
                         GeoTuple3D_F64 b,
                         GeoTuple3D_F64 c)

Computes the cross product:

c = a x b
where 'a' is in homogeneous coordinates.

Parameters:

a - Homogeneous coordinates, z = 1 assumed. Not modified.

b - Not modified.

c - Modified.

cross

public static void cross(GeoTuple2D_F64 a,
                         GeoTuple2D_F64 b,
                         GeoTuple3D_F64 c)

Computes the cross product:

c = a x b

Parameters:

a - Homogeneous coordinates, z = 1 assumed. Not modified.

b - Homogeneous coordinates, z = 1 assumed. Not modified.

c - Modified.

add

public static void add(GeoTuple3D_F64 a,
                       GeoTuple3D_F64 b,
                       GeoTuple3D_F64 c)

Adds two points together.

c = a + b

Point 'c' can be the same instance as 'a' or 'b'.

Parameters:

a - A point. Not modified.

b - A point. Not modified.

c - Where the results are stored. Modified.

add

public static void add(double a0,
                       GeoTuple3D_F64 pt0,
                       double a1,
                       GeoTuple3D_F64 pt1,
                       GeoTuple3D_F64 pt2)

Adds two points together while scaling them.

pt₂ = a₀ pt₀ + a₁ pt₁

Point 'c' can be the same instance as 'a' or 'b'.

Parameters:

a0 - Scaling factor for pt0.

pt0 - A point. Not modified.

a1 - Scaling factor for pt1.

pt1 - A point. Not modified.

pt2 - Where the results are stored. Modified.

addMult

public static <T extends GeoTuple3D_F64> T addMult(T p0,
                                                   org.ejml.data.DenseMatrix64F M,
                                                   T p1,
                                                   T ret)

ret = p0 + M*p1

Parameters:

p0 -

M -

p1 -

ret -

sub

public static void sub(GeoTuple3D_F64 a,
                       GeoTuple3D_F64 b,
                       GeoTuple3D_F64 c)

Substracts two points from each other.

c = a - b

Point 'c' can be the same instance as 'a' or 'b'.

Parameters:

a - A point. Not modified.

b - A point. Not modified.

c - Where the results are stored. Modified.

rotate

public static void rotate(double theta,
                          GeoTuple2D_F64 pt,
                          GeoTuple2D_F64 solution)

Rotates a 2D point by the specified angle.

Parameters:

theta -

pt -

solution - where the solution is written to. Can be the same point as 'pt'.

rotate

public static void rotate(double c,
                          double s,
                          GeoTuple2D_F64 pt,
                          GeoTuple2D_F64 solution)

Rotates a 2D point by the specified angle.

Parameters:

c - Cosine of theta

s - Sine of theta

pt -

solution - where the solution is written to. Can be the same point as 'pt'.

mult

public static <T extends GeoTuple3D_F64> T mult(org.ejml.data.DenseMatrix64F M,
                                                T pt,
                                                T result)

mod = M*pt

pt and mod can be the same reference.

Parameters:

M -

pt -

result - Storage for output. Can be the same instance as param 'pt'. Modified.

mult

public static <T extends GeoTuple2D_F64> T mult(org.ejml.data.DenseMatrix64F M,
                                                GeoTuple3D_F64 pt,
                                                T mod)

mod = M*pt
where mod is a 2D point that has an implicit z=1.

Multiplies the 3x3 matrix against the 3D point, and normalizes the 2D point output by dividing the x and y values by the found z.

mult

public static void mult(org.ejml.data.DenseMatrix64F M,
                        GeoTuple2D_F64 pt,
                        GeoTuple3D_F64 mod)

mod = M*pt
where pt has z=1 implicitly.

Multiplies the 3x3 matrix against the 2D point, which has an implicit z=1 value, and the output is a 3d point.

mult

public static <T extends GeoTuple2D_F64> T mult(org.ejml.data.DenseMatrix64F M,
                                                T pt,
                                                T mod)

Computes mod = M*pt, where both pt and mod are in homogeneous coordinates with z assumed to be equal to 1, and M is a 3x3 matrix.

'pt' and 'mod' can be the same point.

Parameters:

M - 3x3 matrix

pt - Homogeneous point with z=1

mod - Storage for the computation. If null a new point is declared. Can be same instance as pt.

Returns:

Result of computation.

multCrossA

public static org.ejml.data.DenseMatrix64F multCrossA(GeoTuple2D_F64 A,
                                                      org.ejml.data.DenseMatrix64F M,
                                                      org.ejml.data.DenseMatrix64F result)

Computes the following:
result = cross(A)*M
where M and result are 3x3 matrices, cross(A) is the cross product matrix of A.

Parameters:

A - 2D homogenous coordinate (implicit z = 1) that is internally converted into cross product matrix.

M - 3x3 matrix.

result - Storage for results. Can be null.

Returns:

Results.

multCrossA

public static org.ejml.data.DenseMatrix64F multCrossA(GeoTuple3D_F64 A,
                                                      org.ejml.data.DenseMatrix64F M,
                                                      org.ejml.data.DenseMatrix64F result)

Computes the following:
result = cross(A)*M
where M and result are 3x3 matrices, cross(A) is the cross product matrix of A.

Parameters:

A - 3D coordinate that is internally converted into cross product matrix.

M - 3x3 matrix.

result - Storage for results. Can be null.

Returns:

Results.

multTran

public static <T extends GeoTuple3D_F64> T multTran(org.ejml.data.DenseMatrix64F M,
                                                    T pt,
                                                    T mod)

mod = M^T*pt. Both pt and mod can be the same instance.

multTran

public static <T extends GeoTuple3D_F64> T multTran(org.ejml.data.DenseMatrix64F M,
                                                    GeoTuple2D_F64 pt,
                                                    T mod)

mod = M^T*pt
where pt.z = 1 implicitly.

Parameters:

M - 3 by 3 matrix.

pt - 2D point in homogeneous coordinates. Implicit z = 1

mod - 2D point in homogeneous coordinates. Implicit z = 1

Returns:

2D point in homogeneous coordinates. Implicit z = 1

multTran

public static <T extends GeoTuple2D_F64> T multTran(org.ejml.data.DenseMatrix64F M,
                                                    GeoTuple2D_F64 pt,
                                                    T mod)

mod = M^T*pt
where pt.z = 1 implicitly.

Parameters:

M - 3 by 3 matrix.

pt - 2D point in homogeneous coordinates. Implicit z = 1

mod - 2D point in homogeneous coordinates. Implicit z = 1

Returns:

2D point in homogeneous coordinates. Implicit z = 1

innerProd

public static double innerProd(GeoTuple3D_F64 a,
                               org.ejml.data.DenseMatrix64F M,
                               GeoTuple3D_F64 b)

ret = a^T*M*b

Parameters:

a - 3D point.

M - 3 by 3 matrix.

b - 3D point.

Returns:

scalar number

innerProdTranM

public static double innerProdTranM(GeoTuple3D_F64 a,
                                    org.ejml.data.DenseMatrix64F M,
                                    GeoTuple3D_F64 b)

Computes the inner matrix product:
ret = x^TA^Ty

Parameters:

a - 3D point.

M - 3 by 3 matrix.

b - 3D point.

Returns:

scalar number

outerProd

public static org.ejml.data.DenseMatrix64F outerProd(GeoTuple3D_F64 a,
                                                     GeoTuple3D_F64 b,
                                                     org.ejml.data.DenseMatrix64F ret)

Computes the outer product of two vectors:
O = a*b^T

Parameters:

a - 3D vector

b - 3D vector

ret - 3 x 3 matrix or null.

Returns:

outer product of two 3d vectors

addOuterProd

public static org.ejml.data.DenseMatrix64F addOuterProd(org.ejml.data.DenseMatrix64F A,
                                                        double scalar,
                                                        GeoTuple3D_F64 b,
                                                        GeoTuple3D_F64 c,
                                                        org.ejml.data.DenseMatrix64F ret)

Adds the outer product of two vectors onto a matrix:
ret = A + scalar*a*b^T

Parameters:

A - 3x3 matrix

b - 3D vector

c - 3D vector

ret - 3 x 3 matrix or null.

Returns:

outer product of two 3d vectors

innerProd

public static double innerProd(GeoTuple2D_F64 a,
                               org.ejml.data.DenseMatrix64F M,
                               GeoTuple2D_F64 b)

Computes the inner matrix product: ret = a'*M*b
where ret is a scalar number. 'a' and 'b' are automatically converted into homogeneous coordinates.

Parameters:

a - 2D point.

M - 3 by 3 matrix.

b - 2D point.

Returns:

scalar number,

dot

public static double dot(GeoTuple3D_F64 a,
                         GeoTuple3D_F64 b)

Dot product: ret = a^Tb

Parameters:

a - A tuple.

b - A tuple.

Returns:

scalar

scale

public static void scale(GeoTuple3D_F64 p,
                         double v)

Multiplies each element in the tuple by 'v'.
p_i=p_i*v

Parameters:

p - tuple.

v - scaling factor.

changeSign

public static void changeSign(GeoTuple3D_F64 t)

Changes the sign of the vector:

T = -T

Parameters:

t - Vector whose sign is being changed. Modified.

toMatrix

public static org.ejml.data.DenseMatrix64F toMatrix(GeoTuple3D_F64 in,
                                                    org.ejml.data.DenseMatrix64F out)

Converts a GeoTuple3D_F64 into DenseMatrix64F

Parameters:

in - Input vector

out - Output matrix. If null a new matrix will be declared

Returns:

Converted matrix

toTuple3D

public static void toTuple3D(org.ejml.data.DenseMatrix64F in,
                             GeoTuple3D_F64 out)

Converts a DenseMatrix64F into GeoTuple3D_F64

Parameters:

in - Input matrix

out - Output vector.