Analytical Geometry - List of features available in SolidGeometry 5.6

acos2	2D fnct: returns the angle between two vectors including sign
angleintersect	intersect two angle areas
angleinterv	shifts an angle intervall table vainto a fixed interval such as [-pi..+pi] or [0 2*pi]
angleshift	shifts an agle value into a fixed interval such as [-pi..+pi] or [0 2*pi]
aplot	draws an angle relative to a center and two vectors
barycartNT	returns the vertex list (3D) of a point list (2D) relative to one facet
barytocartUVL	converts a 2d Barycentric [u,v] vertex list into a 3D Cartesian coordinate list [x, y, z]
barytocartUVLdelaunay	converts a 2d Barycentric [u,v] vertex list into a 3D Cartesian coordinate list [x, y, z]
cartbaryNT	returns the 2D barycentric coordiantes of a VL relative to one facet
carttobaryVL	converts a 3D planar vertex list into a 2D barycentric coordinate list [u,v]
center3P	Center line of a cylinder given by 3 points
center4P	Center and diameter of a sphere given by 4 points
centerPL	returns the mean of the convex hull of the point list
centerVL	returns the center and distance indices of a vertex list
circ2poly	ratio of polygon radius between if turned pi/n radiands
circlesegmentofPL	returns the angle intervall of a contour PL from a view point A0.
corner2rad	returns the radius based on the distance to the two tangets
CPLisccw	returns index list for CPL direction
CPLrecontour	returns a contour list for a sliced/cutted object
cross2circ	returns the crossing points of two circles
cross2edges	calculates in 2D the crossing point of two straight lines
cross2edges2	calculates in 2D the crossing point of two straight lines
cross2L	returns the crossing point of two straight lines
cross2T	returns 3 crossing points of plane T1 with the plane T2
cross4P	return whether two lines cross each other (2D fnct)
crosscircline	returns the cross points of a circle and a straight line
crossL	returns the crossing points of a stright line with the main planes where z=0, x=0 or y=0
crossT	returns 3 crossing points of a plane TE with the x/y-plane (z=0)
crosstest	return whether a straight line right from point a crosses a line between pa and pb
crosstest2	return whether a straight line right from point a crosses a line between pa and pb
crossz	calculates in 2D only the z-part of the cross product and handles values near zero
CVLremstraight	returns straight points on a line depending on distance and agle
diffTincz	returns for Frames the relative incliniation of the ez vector of B wrt to A
diffTrotz	returns for Frames the relative rotation of the ez vector of B wrt to A
dist2line	mirrors a point at a straight line in 2D
distE	returns shortest distance to x/y plane and normal vector to p
distT	returns orthogonal vector and normal vector to T-plane
dofn	returns the radius relation between a radius and a n-polygon
dofRintrusion	provides the minimum intrusion distance to fully insert a cylinder into a sphere
ELdirectVLEL	returns a edge list, in which all contours have the same direction than the first contour in the edge list
ezof3P	returns ez and R for 3 Point Rotation Matrix
getprojectionimage	returns a single projection image of gca
hesseplaneofT	Hessennormalform of T's xy plane
imageofVLprojection	returns an image of a VL projection using the matlab camera view concept
insidePLELdelaunay	returns whether a point is inside/outside a contour
intersectstriangle	fundamental fnct for the intersection between a ray and a triangle
intersectstriangle46	fundamental fnct for the intersection between a ray and a triangle
isincirclesegment	returns whether an angle or a angle list is inside an angle interval
isintriangle2	returns whether a point is in a triangle
isrealr	returns whether all elements on a row are real
issameside	return whether 2 points p1,p2 are on the same side of a line through A to B
KDWofXY	returns two line distances of points and an angle and a displacement of a straigt line line from two points
lengthC	returns length and maximum of changing angle plus
mirroringatline	mirrors a point at a straight line in 2D
mirroringatline3D	mirrors a point at a straight line in 3D
nearestcluster	returns a reduced list of points and a cluster list
nearestpair	returns the nearest point pairs of two vector list
NLconformance	changes the orientation of a list of normal vectors
NLcontourVL	return the list of normal vector for the edges between the vertices and the vertices between the edges
nofrd	returns the minimum number of edges to guarante a slot distance between a peg and a hole
phiofsr	returns a angle difference to achieve a slot size
planedistanceofT	returns the distance of a vertex list to a plane in HT coordinate form
planeparamofT	returns the plane parameters from a HT matrix (x/y plane) - ax+by+cz+d=0
PLcircle	returns a 2D point list of a circle or circle segment
PLevolvente	returns the point list of an evolvente curve
PLFLfaceNormal	returns the rounded (1e-5) length of the area size/length of normal vector
PLFLofCPLdelaunay	Returns 2D point list and facet list of a triangulated contour
PLFLofCPLpoly	Utilizes the poly2fv fnct for VLFL-LIb
PLnorm	returns a normalize vector list nx2
plotT	plots a coordinate system given as HT matrix
projectionimage	returns a central projection image by using Matlabs view commands
RL2exl	returns X vectors for a list of euler angles
RLcurvature	returns a circular bended closed contour
RLofEulerInterpolation	Returns euler rotations as linear interpolation
RLplot	plots along the z axis the systems of a Euler Rotation List
rofcircbend	returns bending radius and angle for a compressed line
Rofez	returns a rotation matrix based on a list of ez vector
Rofrdintrusion	provides the minimum intrusion distance to fully insert a cylinder into a sphere
rofRintrusion	provides the minimum intrusion distance to fully insert a cylinder into a sphere
Rofxy	Rotation matrix by the ez vektor and and optional rotation angle
rot	returns rotation matrix in 3x3 as Rx*Ry*Rz or 2x2 Rz
rotdeg	returns 3x3 rotation matrix for Deg angles in x, y, z
RPofTrelT	returns the frame T2 in relation to frame T1
screw2R	definition of a screw coordinate system
setgcapixelsize	sets the current gca to a default pixelsize
SGClayout	returns a modified arranged solid table
SGcutTbladeangle	returns the mean center angle of the cutting blades
SGgetCenterPoint	returns a point in the center of all vertices
SGmagnifyVL	magnifies/shrinks the dimensions of the vertex list
SGmirrorD	Mirrors a solid in a distance to the maximal dimension in the specified direction
SGrotate4print	rotates an object to achieve as long as possible lines on the floot
SGsurfacedistance	calculates the shift distance from a solid to the surface of another solid
SGvolume	returns the estimated volume of a solid
sizePLFL	returns the index of facets with area > 0
sofrd	returns the minimal auxiliary point distance on a circular curved contour
tangent2circ	returns outer and inner tangents of 2 circles
tangente	returns the point for a tangente
tangentRP	returns the two tangential points of a circle
Tcross2T	returns the crossing line HT of two defined planes T1 and T2
textP	draws a texlabel text at the position
textT	drawn a text at the position of a HT matrix
TflipR	turns the current right hand system into an inverted left hand system
tfplot	plots an HT matrix including the x/y plane
THLof2F	returns Tetrahedron list of two facets
TLofCVL	returns a list of frames that connect a start frame and an end frame along a spatial contour
Tof2vec	returns transformation matrix based on the 2 point movements
TofcamVLPL	returns the coordinate system and calibration matrix of a camera
TofDPhiH	returns a 4x4 transformation matrix
Tofgca	returns the HT matrix of the current camera position
Tofhesseplane	returns an HT amtrix from a hesse normal form of a plane
TofP	returns a T matrix from a point in 2D or 3D
TofPcam	returns a transformation matrix using a vertex and a the current camera view
TofPEul	return from euler angle and position an HT matrix
TofPez	creates a T matrix from point and ez-Vector
TofSG	sets a HT matrix relativ to nested solid
TofSGML	returns HT for a mounting face with known number
TofSGMLez	returns HT for a mounting face with known ez
TofT	returns a T matrix defined relative to another T matrix
TofTrel	creates a HT matrix relative to a frame
TofVL	returns the main axis of a vertex list or SG
TPL	return for vertices of a patch the HT Matrix of the patch center
TplanesofPCnormals	returns the HT matrices for the points and normals
TplanesofVLFLfacets	returns the HT matrices for the facets from center and normal
tplot	plots a coordinate system given as HT matrix
TregisterConvexHull	returns the registration matrix based on the convex hull of the vertices
Txy	returns a matrix for a point p and pitch-yaw values of ez
vec2number	converst a vector row into a number for vector elemetns of 1 to 9
vec2ortho	creates the orthogonal vectors for a 2D vector list
vecnormr	returns for a vector list (rows) the vectnorm result
VLBezier4P	simple fnct to calculate a 3D Bezier curve
VLBezierC	returns a Bezier curve for a given list of points
VLcross2Lines3D	returns the crossing point of 2 lines in [x y z]
VLcrossstraightnline3D	returns the crossing point of 2 lines in [x y z]
VLdistance	returns a distance list - but is different from VLnorm
VLFLfaceNormal	returns the normal vector (or NAN) of the facet list and cutted (1e-4) length
VLFLmeshdensity	decreases the edge length of the facets for deformation use
VLFLrotsymRLELn	returns VL and FL for a torus style solid
VLFLspherecurvedCL	returns VL and FL for a sphere curved surface given by a 2D contour point list
VLFLspherecurvedGPL	returns a sphere curved (3D) contoured surface grid (2D)
VLFLvertexNormal	returns the vertex normal for the vertices of a solid
VLGraham	returns the convex hull of a point list by Graham (outdated)
VLGrahamPVL	returns the convex hull for a given set of vertices that are in a plane
VLinsertEulerSteps	inserts vertex points on straight lines if the twist angle is to large
VLmindist	returns the minimal distance larger than zero
VLmindxyz	returns the minimal distance larger than zero
VLmostdistanceNeighborN	return a list of n points ou of a points list that have the maximum distance sum
VLnearestNeighborN	returns the N nearest Neighbors between two point lists
VLNLplot	plots a normal vector list at a vertex list
VLofimsegthres	returns a VL of segmented points within an image
VLplaneprojection	returns a PL as projection of a vertex list to a orthogal plane defined by an ez vector
VLprojection2SG	projects a Vertex list in parallel projection to a solid
VLRadius4P	returns a contour based on 4 points similar to VLBezier4P
VLseparate	wish to solve boolean opeartion problems
VLtangentcirc	creates a vertex list for a tangential circle segment
wofcross2circ	just returns the angles of the two crosspoints
wofT	returns simply the squeezed atan2 of the rotation matrix of T
zigzag	returns a zig zag curve in the interval [0 2*pi]