GHL Version 3.4.4 Function List

Table of Contents

• Entities and Modules
• Geometric evaluation (2D/3D)
• Intersection/Interference (2D/3D)
• Angle (2D/3D)
• Distance (2D/3D)
• Shortest Distance (2D)
• Side (2D/3D)
• Projection (2D/3D)
• Common Normal(2D/3D)
• Tangent (2D/3D)
• Common tangent (2D)
• Element creation (2D/3D)
• Fillet insertion (2D/3D)
• Offsetting (2D/3D)
• Sweeping/Skinning (3D)
• Line Segment operations (2D)
• Freeform operations (2D/3D)
• Composite Curve operations (2D/3D)
• Pseudo embedded graph(2D)
• Voronoi diagram / Delaunay diagram(2D)
• Set of triangles(2D/3D)
• (closed) Polygon(2D)
• S-patch(3D)
• Printing(2D/3D)
• Coordinate transformation (2D/3D)
• Vector operation (2D/3D)
• Equation
• Polynomial
• Matrix
• Others

Entities and Modules

Pnt	Point					Pln	Plane
Vec	Vector					Sph	Spherical surface
Axp	Local coordinate system			Cyl	Cylindrical surface
Lin	Line					Con	Conical surface
Lsg	Line segment (poly line)		Bzs	Bezier surface (polynom./rational)
Cir	Circle					Bss	Bspline surace (polynom./rational)
Ell	Ellipse					Les	Surface of linear extrusion
Par	Parabola				Rvs	Surface of revolution
Hyp	Hyperbola				Rts	Rectangular trimmed surface
Bzc	Bezier curve (polynom./rational)	Cbs	Curve bounded surface
Bsc	Bspline curve (polynom./rational)	GS	S Patch
Trc	Trimmed curve
Cmc	Composite curve

GHL 3.4.4 is supplied as following sets(2D Subset or Fullset) which are combination of above mentioned entities.

Subset name	Entities
----------------------------------------------------------------------------------
2D Subset	2D Elements(Point/Vector/Axis Placement/Curve) + Utilities
Fullset		2D Subset + 3D Elements(Point/Vector/Axis Placement/Curve/Surface)

Geometric evaluation (2D/3D)

Get various geometric characteristics of an geometric element

• Evaluate a curve at a parameter (position, tangent vector, curvature, principal normal, tosion)
• Evaluate a surface at a pair of parameters (position, first/second partial derivatives, principal curvatures)
• Determine the length of curve
• Determine the area of curve
• Determine the enclosing box of curve
• Get the cusp points of curve
• Get the singular points of free-form curve
• Get the inflection points of free-form curve
• Get a self-intersection of free-form curve, line segment

Intersection/Interference (2D/3D)

Get all the intersections of two curves

	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Lsg	Trc	Cmc
Lin	x	-	-	-	-	-	-	-	-	-
Cir	x	x	-	-	-	-	-	-	-	-
Ell	x	x	x	-	-	-	-	-	-	-
Par	x	x	x	x	-	-	-	-	-	-
Hyp	x	x	x	x	x	-	-	-	-	-
Bzc	x	x	x	x	x	x	-	-	-	-
Bsc	x	x	x	x	x	x	x	-	-	-
Lsg	x	x	x	x	x	x	x	x	-	-
Trc	x	x	x	x	x	x	x	x	x	-
Cmc	x	x	x	x	x	x	x	x	x	x

Get all the intersections of curve and surface

	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Trc	Cmc
Pln	x	x	x	x	x	x	x	x	x
Sph	x	x	x	x	x	x	x	x	x
Cyl	x	x	x	x	x	x	x	x	x
Con	x	x	x	x	x	x	x	x	x
Bzs	x	x	x	x	x	x	x	x	x
Bss	x	x	x	x	x	x	x	x	x
Les	x	x	x	x	x	x	x	x	x
Rvs	x	x	x	x	x	x	x	x	x
Cbs	x	x	x	x	x	x	x	x	x

Get all the intersections of two surfaces

	Pln	Sph	Cyl	Con	Bzs	Bss	Les	Rvs	Cbs
Pln	x	-	-	-	-	-	-	-	-
Sph	x	x	-	-	-	-	-	-	-
Cyl	x	x	x	-	-	-	-	-	-
Con	x	x	x	x	-	-	-	-	-
Bzs	x	x	x	x	x	-	-	-	-
Bss	x	x	x	x	x	x	-	-	-
Les	x	x	x	x	x	x	x	-	-
Rvs	x	x	x	x	x	x	x	x	-
Cbs	x	x	x	x	x	x	x	x	x

Get all the interference of two curves

	Bzc	Bsc	Lsg	Trc	Cmc
Bzc	x	-	-	-	-
Bsc	x	x	-	-	-
Lsg	-	-	x	-	-
Trc	-	-	-	x	-
Cmc	-	-	-	-	x

Get all the interference of two surfaces

	Pln	Bzs	Bss
Pln	-	-	-
Bzs	x	x	-
Bss	x	x	x

Angle (2D/3D)

Get the angle between two geometric elements

	Lin	Pln
Lin	x	-
Pln	x	x

Distance (2D/3D)

Get the distance between two geometric elements

	Pnt	Lin
Pnt	x	-
Lin	x	x

Shortest Distance(2D)

Get the shortest distance between a point and a curve

• Curve : Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Lsg/Trc/Cmc

Get the shortest distance between two curves

	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Lsg	Trc	Cmc
Lin	x	-	-	-	-	-	-	-	-	-
Cir	x	x	-	-	-	-	-	-	-	-
Ell	x	x	x	-	-	-	-	-	-	-
Par	x	x	x	x	-	-	-	-	-	-
Hyp	x	x	x	x	x	-	-	-	-	-
Bzc	x	x	x	x	x	x	-	-	-	-
Bsc	x	x	x	x	x	x	x	-	-	-
Lsg	x	x	x	x	x	x	x	x	-	-
Trc	x	x	x	x	x	x	x	x	x	-
Cmc	x	x	x	x	x	x	x	x	x	x

Side (2D/3D)

Judge whether a point is on other elements

• Entity : Pnt/Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Cmc/Pln

Judge in which side of curve a point lies

• Curve : Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Cmc

Projection (2D/3D)

Get all the feet of perpendicular from a point to geometric element

• Curve : Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Cmc
• Surface : Pln/Sph/Cyl/Con/Bzs/Bss/Les/Rvs/Cbs

Project a curve to a plane

• Curve : Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Lsg/Trc/Cmc

Common Normal(2D)

Get all the common normals of two geometric elements

	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Lsg	Trc	Cmc
Lin	x	-	-	-	-	-	-	-	-	-
Cir	x	x	-	-	-	-	-	-	-	-
Ell	x	x	x	-	-	-	-	-	-	-
Par	x	x	x	x	-	-	-	-	-	-
Hyp	x	x	x	x	x	-	-	-	-	-
Bzc	x	x	x	x	x	x	-	-	-	-
Bsc	x	x	x	x	x	x	x	-	-	-
Lsg	x	x	x	x	x	x	x	x	-	-
Trc	x	x	x	x	x	x	x	x	x	-
Cmc	x	x	x	x	x	x	x	x	x	x

Tangent (2D)

Get all the tangential points from a point to curve

• Curve : Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Cmc

Common tangent (2D)

Get all the common tangents of two curves

	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Trc	Cmc
Lin	x	-	-	-	-	-	-	-	-
Cir	x	x	-	-	-	-	-	-	-
Ell	x	x	x	-	-	-	-	-	-
Par	x	x	x	x	-	-	-	-	-
Hyp	x	x	x	x	x	-	-	-	-
Bzc	x	x	x	x	x	x	-	-	-
Bsc	x	x	x	x	x	x	x	-	-
Trc	x	x	x	x	x	x	x	x	-
Cmc	x	x	x	x	x	x	x	x	x

Element creation (2D/3D)

• Create a line from 2 points
• Create a conic section (Cir/Ell/Par/Hyp) from 5 points
• Create a tangential circle of 3 entities(Pnt/Lin/Cir)(2D)
• Interpolate a polygon with free-form curve (Bsc)
• Approximate a polygon with free-form curve (Bzc/Bsc)
• Interpolate a polynet with free-form surface (Bss)
• Interpolate boundaries with free-from surface (Bss)
• Approximate a polynet with free-form surface (Bzs/Bss)
• Convert a curve into line-segment
• Convert a curve into rational free-form curve (Bzc/Bsc)
• Convert a surface into rational free-form surface (Bzs/Bss)
• Get an isoparametric curve of surface
• Convert a surface into set of triangle
• Convert a Bzs/Bss into grid points
• Reduce the number of segments of a Bss

Fillet insertion (2D/3D)

Insert fillets between two 2D geometric elements

	Pnt	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc	Trc
Pnt	x	-	-	-	-	-	-	-	-
Lin	x	x	-	-	-	-	-	-	-
Cir	x	x	x	-	-	-	-	-	-
Ell	x	x	x	x	-	-	-	-	-
Par	x	x	x	x	x	-	-	-	-
Hyp	x	x	x	x	x	x	-	-	-
Bzc	x	x	x	x	x	x	x	-	-
Bsc	x	x	x	x	x	x	x	x	-
Trc	x	x	x	x	x	x	x	x	x

Insert fillets between two 3D geometric elements

	Pnt	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc
Pnt	x	-	-	-	-	-	-	-
Lin	x	x	-	-	-	-	-	-
Cir	x	x	x	-	-	-	-	-
Ell	x	x	x	x	-	-	-	-
Par	x	x	x	x	x	-	-	-
Hyp	x	x	x	x	x	x	-	-
Bzc	x	x	x	x	x	x	x	-
Bsc	x	x	x	x	x	x	x	x

	Pnt	Lin	Cir	Ell	Par	Hyp	Bzc	Bsc
Pln	x	x	x	x	x	x	x	x
Sph	x	x	x	x	x	x	x	x
Cyl	x	x	x	x	x	x	x	x
Con	x	x	x	x	x	x	x	x
Bzs	x	x	x	x	x	x	x	x
Bss	x	x	x	x	x	x	x	x
Les	x	x	x	x	x	x	x	x
Rvs	x	x	x	x	x	x	x	x
Cbs	x	x	x	x	x	x	x	x

	Pln	Sph	Cyl	Con	Bzs	Bss	Les	Rvs	Cbs
Pln	x	-	-	-	-	-	-	-	-
Sph	x	x	-	-	-	-	-	-	-
Cyl	x	x	x	-	-	-	-	-	-
Con	x	x	x	x	-	-	-	-	-
Bzs	x	x	x	x	x	-	-	-	-
Bss	x	x	x	x	x	x	-	-	-
Les	x	x	x	x	x	x	x	-	-
Rvs	x	x	x	x	x	x	x	x	-
Cbs	x	x	x	x	x	x	x	x	x

Offsetting (2D/3D)

Offset a geometric element

• 2D element : Pnt/Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Cmc
• 3D element : Pnt/Lin/Cir/Ell/Par/Hyp/Bzc/Bsc/Trc/Pln/Sph/Cyl/Con/Bzs/Bss/Les/Rvs/Cbs

Sweeping/Skinning(3D)

Sweeping

• input: Bsc, RBsc
• output: Bss, RBss

Skinning

• input: Bsc, RBsc
• output: Bss, RBss

Line Segment operations(2D)

• Divide a line segment into two
• Trancate a line segment
• Reverse the direction of a line segment
• Judge the direction of a closed line segment

Freeform operations (2D/3D)

• Elevate the degree of Bzc/Bzs
• Divide a Bzc/Bzs into two
• Get the monomial form of Bzc
• Evaluate Bernstein functions at a parameter
• Elevate the degree of Bsc/Bss
• Insert a knot into Bsc/Bss
• Divide a Bsc/Bss into two
• Convert a Bsc/Bss into Bzc/Bzs
• Get the monomial form of Bsc
• Evaluate Bspline functions at a parameter
• Get the index of a Bspline segment that includes a given parameter
• Get the value of i-th knot
• Blossoming
• Judge whether a Bzs is planar or not
• etc.

Composite Curve operations(2D/3D)

• Add a trimmed curve at the end of a composite curve
• Count the number of trimmed curve in a composite curve
• Return the i-th trimmed curve in a composite curve
• Add a trimmed curve at a given point of a composite curve
• Get the segment of a composite curve
• remove self-intersection of closed composite curve(2D)
• set operation of closed composite curve(2D)
• etc.

Pseudo embedded graph(2D)

• add vertices/edges/faces into a pseudo embedded graph
• remove vertices/edges/faces from a pseudo embedded graph
• attach arbitrary data to a vertex/edge/face
• call specified function for each of vertices/edges/faces
• etc.

Voronoi diagram / Delaunay diagram(2D)

• generate Voronoi/Delaunay diagram for a set of points
• attach arbitrary data to a vertex/edge/face
• etc.

Set of triangles(2D/3D)

• generate a triangulation for a set of points
• attach arbitrary data to a vertex/edge/face
• call specified function for each of vertices/edges/faces
• etc.

(closed) Polygon(2D)

• judge whether a set of points is included by a closed polygon or not
• determine the loop-wise (CW/CCW) of closed polygon
• do set operation (sum/intersection) for 2 closed polygons
• etc.

S-patch(3D)

• Allocate an empty s-patch
• Approximate s-patch with Set of Triangle
• Approximate s-patch with Bezier Surfaces
• Evaluate s-patch
• Create Gregory s-patch
• Free s-patch
• Depth elevation for normal s-patch
• Get normal vector of s-patch

Printing(2D/3D)

• Set/Get the function for printing a string
• Set/Get the number of decimal columns for floating point numbers
• Print the type of entity
• Print the definition of entity

Coordinate transformation (2D/3D)

• Transform a point/vector into enclosing coordinate system
• Transform a point/vector into local coordinate system

Vector operation (2D/3D)

• Get the norm of vector
• Unitize a vector
• Get the sum/difference/dot product/cross product of two vectors
• Sum vectors with weights
• Generate a vector which is perpendicular with a given vector

Equation

• Solve a quadric equation (real, complex)
• Solve n-th degree equation by Durand-Kerner method (complex)
• Solve n-th degree equation by Newton-Raphson method (real, complex)
• Solve simultaneous non-linear equations by Newton-Raphson method
• Integrate the specified function over finite interval

Polynomial

• Cross product of position and 1st derivative of a vector polynomial
• Cross product of 1st and 2nd derivatives of a vector polynomial
• Evaluate a real polynomial
• Evaluate a complex polynomial
• Multiply a polynomial by another polynomial
• Transform a vector polynomial into [0, 1] unit parameter section

Matrix

• LU-decomposition of N * N matrix
• Solver of LU-decomposed linear equations
• Compute linear least square solutions

Others

• Array management
• List management
• Binary-Tree/N-ary-Tree management
• Initialize various tolerance values
• Judge whether given points are collinear or not
• Judge whether given points are coplanar or not
• Translate a geometric element
• Rotate a geometric element
• Extend/contract a geometric element
• Convert a vector into slope angle in radian
• Normalize angle into [(0, 2pi)]
• Maximum/Minimum value in the arguments
• Coefficient of Pascal triangle
• Greatest Common Divider, Least Common Multiple
• etc.