vect3d

README

#vect3d#

Package csvrec implements several 3d vector functions.

Documentation

Overview

Package vect3d implements several 3d vector functions.

Index

• func Add(a, b [3]float64) (result [3]float64)
• func CrossProduct(a, b [3]float64) (result [3]float64)
• func DistPt2Line(a, n, b [3]float64) float64
• func DistPt2Pt(a, b [3]float64) float64
• func DotProduct(veca, vecb [3]float64) float64
• func GetAngle(a, b [3]float64) float64
• func GetComplexRotationMatrix(xAngle, yAngle, zAngle float64) (Q [][]float64)
• func GetRotationMatrix(axis [3]float64, angle float64) (Q [][]float64)
• func GetSignedAngle(a, b, axis [3]float64) float64
• func Magnitude(vec [3]float64) float64
• func Make2D(r, c int) (A [][]float64)
• func Make3D(r, c, d int) (A [][][]float64)
• func NearestPtOnLine(a, n, b [3]float64) [3]float64
• func Normalize(a [3]float64) [3]float64
• func ReflectX(a [3]float64) (b [3]float64)
• func ReflectY(a [3]float64) (b [3]float64)
• func ReflectZ(a [3]float64) (b [3]float64)
• func Rotate3D(A [3][3]float64, b [3]float64) (c [3]float64)
• func RotateAxis(a, origin, axis [3]float64, angle float64) (b [3]float64)
• func RotateN1N2(a, origin, n1, n2 [3]float64, angle float64) (b [3]float64)
• func RotateN1N2N3(a, origin, n1, n2, n3 [3]float64, angle float64) (b [3]float64, err error)
• func RotateTransPt(a, origin, trans [3]float64, Q [][]float64) (b [3]float64)
• func RotateX(a, origin [3]float64, angle float64) (b [3]float64)
• func RotateY(a, origin [3]float64, angle float64) (b [3]float64)
• func RotateZ(a, origin [3]float64, angle float64) (b [3]float64)
• func ScalerMult(a [3]float64, b float64) (result [3]float64)
• func Subtract(a, b [3]float64) (result [3]float64)
• func Translate(a, dir [3]float64) (b [3]float64)
• func TranslateDist(a, dir [3]float64, dist float64) (b [3]float64)
• func Transpose2dFloat(A [][]float64) (B [][]float64, err error)
• func TriNormal(n1, n2, n3 [3]float64) [3]float64
• func YawPitchRoll(yaw, pitch, roll float64, pt [3]float64) (rotpt [3]float64)

Functions

func Add

func Add(a, b [3]float64) (result [3]float64)

Add returns the 3d vector a + b

func CrossProduct

func CrossProduct(a, b [3]float64) (result [3]float64)

CrossProduct returns the crossproduct of a and b a and b are 3d vectors

func DistPt2Line

func DistPt2Line(a, n, b [3]float64) float64

DistPt2Line returns the shortest distance from b to the line defined by a and n a is a point on the line n is the vector of the line b is a point not on the line The result is the shortest distance from b to the line

func DistPt2Pt

func DistPt2Pt(a, b [3]float64) float64

DistPt2Pt returns the distance from 3d point a to 3d point b a is a point b is another point The result is the shortest distance from b to the line

func DotProduct

func DotProduct(veca, vecb [3]float64) float64

DotProduct returns the dot product of 3d vectors a and b.

func GetAngle

func GetAngle(a, b [3]float64) float64

GetAngle returns cos(theta) where theta is the angle between 3d vectors a and b.

func GetComplexRotationMatrix

func GetComplexRotationMatrix(xAngle, yAngle, zAngle float64) (Q [][]float64)

GetComplexRotationMatrix returns a compound rotation matrix for rotating about the x, y, and z axis respectively.

func GetRotationMatrix

func GetRotationMatrix(axis [3]float64, angle float64) (Q [][]float64)

GetRotationMatrix returns the Q matrix needed for RotateTransPt

func GetSignedAngle

func GetSignedAngle(a, b, axis [3]float64) float64

GetSignedAngle returns the signed angle theta (radians) between 3d vectors a and b about the given the axis.

func Magnitude

func Magnitude(vec [3]float64) float64

Magnitude returns the magnitude of a 3d vector.

func Make2D

func Make2D(r, c int) (A [][]float64)

Make2D creates a slice of dimension [r][c]. In terms of a matrix, this is analogous to an r row by c column matrix.

func Make3D

func Make3D(r, c, d int) (A [][][]float64)

Make3D creates a slice of dimension [r][c][d]. In terms of a matrix, this is analogous to an r row by c column by d depth matrix.

func NearestPtOnLine

func NearestPtOnLine(a, n, b [3]float64) [3]float64

NearestPtOnLine returns the point on a line defined by point a and normalized vector n that is closest to b a is a point on the line n is the NORMALIZED vector of the line b is a point not necessarily on the line

func Normalize

func Normalize(a [3]float64) [3]float64

Normalize returns a/|a| where a is a 3d vector

func ReflectX

func ReflectX(a [3]float64) (b [3]float64)

ReflectX moves a point to its mirrored location about the X plane a is the point to be moved b is the moved point

func ReflectY

func ReflectY(a [3]float64) (b [3]float64)

ReflectY moves a point to its mirrored location about the X plane a is the point to be moved b is the moved point

func ReflectZ

func ReflectZ(a [3]float64) (b [3]float64)

ReflectZ moves a point to its mirrored location about the X plane a is the point to be moved b is the moved point

func Rotate3D

func Rotate3D(A [3][3]float64, b [3]float64) (c [3]float64)

Rotate3D rotates vector b by rotation matrix A. This is matrix multiplication of size 3x3 X 3x1 = 3x1.

func RotateAxis

func RotateAxis(a, origin, axis [3]float64, angle float64) (b [3]float64)

RotateAxis rotates a point a about an origin and an axis a specified angle (radians) a is the point to be moved b is the moved point It doesn't require the axis to be normalized.

func RotateN1N2

func RotateN1N2(a, origin, n1, n2 [3]float64, angle float64) (b [3]float64)

RotateN1N2 rotates a point a about an origin and an axis, formed by n2-n1, a specified angle (radians) a is the point to be moved b is the moved point

func RotateN1N2N3

func RotateN1N2N3(a, origin, n1, n2, n3 [3]float64, angle float64) (b [3]float64, err error)

RotateN1N2N3 rotates a point around an origin in the plane specified by three points in the plane (n1, n2, and n3) a is the point to be moved b is the moved point

func RotateTransPt

func RotateTransPt(a, origin, trans [3]float64, Q [][]float64) (b [3]float64)

RotateTransPt rotates a point given a rotation matrix Q, and an origin and translates it by trans

func RotateX

func RotateX(a, origin [3]float64, angle float64) (b [3]float64)

RotateX rotates point a about the given origin and X axis a specified angle (radians) a is the point to be moved b is the moved point

func RotateY

func RotateY(a, origin [3]float64, angle float64) (b [3]float64)

RotateY rotates point a about the given origin and Y axis a specified angle (radians) a is the point to be moved b is the moved point

func RotateZ

func RotateZ(a, origin [3]float64, angle float64) (b [3]float64)

RotateZ rotates point a about the given origin and Z axis a specified angle (radians) a is the point to be moved b is the moved point

func ScalerMult

func ScalerMult(a [3]float64, b float64) (result [3]float64)

ScalerMult returns a * b a is three dimensional vector b is a scalar

func Subtract

func Subtract(a, b [3]float64) (result [3]float64)

Subtract returns the 3d vector a - b

func Translate

func Translate(a, dir [3]float64) (b [3]float64)

Translate moves a 3d point a along the vector dir to 3d point b a is the point to be moved b is the moved point dir is a vector representing the direction and distance a is moved.

func TranslateDist

func TranslateDist(a, dir [3]float64, dist float64) (b [3]float64)

TranslateDist moves a 3d point a along the vector dir a distance d to 3d point b a is the point to be moved b is the moved point dir is a vector representing the direction and distance a is moved.

func Transpose2dFloat

func Transpose2dFloat(A [][]float64) (B [][]float64, err error)

Transpose2dFloat creates the transpose of a rectangular 2-dimensional slice of type float64 as if it were a transposable matrix.

func TriNormal

func TriNormal(n1, n2, n3 [3]float64) [3]float64

TriNormal returns the normal of a triangle with a normal that is the cross product of n2 - n1 and n3 - n2

func YawPitchRoll

func YawPitchRoll(yaw, pitch, roll float64, pt [3]float64) (rotpt [3]float64)

YawPitchRoll rotates a point through yaw, pitch, and roll, in that order according to the Tait-Bryan z-y'-x” intrinsic rotation convention. yaw, pitch, and roll are entered in degrees with bounds: -360 < yaw < 360; -360 < pitch < 360; -360 < roll < 360. pt is the point to be rotated. rotpt is the rotated point.