Functions.md

Functions

CurrentModule = Modia3D

3D Vectors

Functions to construct 3D vectors v::SVector{3,F}.

ZeroVector3D
axisValue

Rotation Matrices

Functions to construct rotation matrices R::SMatrix{3,3,F,9} rotating a coordinate-system/frame 1 into a coordinate-system/frame 2.

Function	Description
Modia3D.NullRotation(::Type{F})	No rotation from frame 1 to frame 2
Modia3D.assertRotationMatrix(R)	Assert that R is a rotation matrix
Modia3D.rot1(angle)	Rotate around angle along x-axis
Modia3D.rot2(angle)	Rotate around angle along y-axis
Modia3D.rot3(angle)	Rotate around angle along z-axis
Modia3D.rot123(angle1, angle2, angle3)	Rotate around angles along x,y,z-axes
Modia3D.rot123(angles)	Rotate around angles along x,y,z-axes
Modia3D.rotAxis(axis,angle)	Rotate around angle along axis (= 1,2,3)
Modia3D.rotAxis(axis,positive,angle)	Rotate around angle if positive, else -angle
Modia3D.rot_e(e, angle)	Rotate around angle along unit vector e
Modia3D.rot_nxy(nx, ny)	nx/ny are in x/y-direction of frame 2
Modia3D.rot_nxz(nx, nz)	nx/nz are in x/z-direction of frame 2
Modia3D.from_q(q)	Return rotation matrix from quaternion q

Examples

using Modia3D

# R1,R2,R3 are the same RotationMatrices
R1 = Modia3D.rot1(pi/2)
R2 = Modia3D.rot1(90u"°")
R3 = Modia3D.rot_e([1,0,0], pi/2)

NullRotation
assertRotationMatrix
rot1
rot2
rot3
rot123
rotAxis
rot_e
rot_nxy
rot_nxz
from_q

Quaternions

Functions to construct quaternions q::SVector{4,F} rotating a coordinate-system/frame 1 into a coordinate-system/frame 2.

Function	Description
Modia3D.NullQuaternion(::Type{F})	No rotation from frame 1 to frame 2
Modia3D.assertQuaternion(q)	Assert that q is a quaternion
Modia3D.qrot1(angle)	Rotate around angle along x-axis
Modia3D.qrot2(angle)	Rotate around angle along y-axis
Modia3D.qrot3(angle)	Rotate around angle along z-axis
Modia3D.qrot123(angle1, angle2, angle3)	Rotate around angles along x,y,z-axes
Modia3D.qrot_e(e, angle)	Rotate around angle along unit vector e
Modia3D.qrot_nxy(nx, ny)	nx/ny are in x/y-direction of frame 2
Modia3D.qrot_nxz(nx, nz)	nx/nz are in x/z-direction of frame 2
Modia3D.from_R(R)	Return q from rotation matrix R

NullQuaternion
assertQuaternion
qrot1
qrot2
qrot3
qrot123
qrot_e
qrot_nxy
qrot_nxz
from_R

Frame Transformations

Functions to transform vectors, rotation matrices, quaternions between coordinate systems and functions to determine properties from coordinate system transformations.

Function	Description
Modia3D.resolve1(rot, v2)	Transform vector v from frame 2 to frame 1
Modia3D.resolve2(rot, v1)	Transform vector v from frame 1 to frame 2
Modia3D.absoluteRotation(rot01, rot12)	Return rotation 0->2 from rot. 0->1 and 1->2
Modia3D.relativeRotation(rot01, rot02)	Return rotation 1->2 from rot. 0->1 and 0->2
Modia3D.inverseRotation(rot01)	Return rotation 1->0 from rot, 0->1
Modia3D.planarRotationAngle(e,v1,v2)	Return angle of planar rotation along e
Modia3D.eAxis(axis)	Return unit vector e in direction of axis
Modia3D.skew(v)	Return skew-symmetric matrix of vector v

resolve1
resolve2
absoluteRotation
relativeRotation
inverseRotation
planarRotationAngle
eAxis
skew

Frame Interpolations

Given a set of coordinate-systems/frames by a vector r of position vectors (to their origins) and and an optional vector q of Quaternions (of their absolute orientations), then the following functions interpolate linearly in these frames:

Function	Description
Modia3D.Path(r,q)	Return path defined by a vector of frames
Modia3D.t_pathEnd(path)	Return path parameter t_end of last frame
Modia3D.interpolate(path,t)	Return (rt,qt) of Path at path parameter t
Modia3D.interpolate_r(path,t)	Return rt of Path at path parameter t

Path
t_pathEnd
interpolate
interpolate_r