jv.vecmath

Class PuVectorGeom

• java.lang.Object
• jv.vecmath.PuVectorGeom

• public class PuVectorGeom
extends java.lang.Object
Static methods for vector geometry. Most methods work in euclidean vector spaces of arbitrary dimension.
• Constructor Detail

• PuVectorGeom

public PuVectorGeom()
• Method Detail

• intersectionOfLineAndLine

public static double intersectionOfLineAndLine(PdVector p,
PdVector base1,
PdVector dir1,
PdVector base2,
PdVector dir2)
Check for intersection of line and line by solving equation b1+sd1 = b2+td2. Multiply both sides with d1 and with d2 to obtain two scalar equations
+ s =  + t
+ s =  + t
=> s = d2>/(1.-**2)

Method works in euclidean vector spaces of arbitrary dimension.
Parameters:
p - computed intersection point
base1 - any point on the first line
dir1 - unit direction of first line
base2 - any point on the second line
dir2 - unit direction of second line
Returns:
double distance s from base1 to intersection point, or Double.MAX_VALUE if line and plane are parallel.
• intersectionOfLineAndPlane

public static double intersectionOfLineAndPlane(PdVector p,
PdVector base1,
PdVector dir,
PdVector base2,
PdVector normal)
Compute intersection line and plane. Line is given by base point and direction, plane is given by base point and plane normal. The intersection point x=ray+s*dir on the line must fulfill plane equation = . Use this equation to derive a value for s by solving = leading to s = /. Direction of ray must be normalized, normal of plane need not be normalized.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
p - computed intersection point
base1 - any point on the line
dir - unit direction of line
base2 - any point on the plane
normal - normal of plane, need not be normalized
Returns:
double distance s from base1 to intersection point, or Double.MAX_VALUE if line and plane are parallel.
• intersectionOfPlaneAndPlane

public static boolean intersectionOfPlaneAndPlane(PdVector lineBase,
PdVector lineDir,
PdVector base1,
PdVector normal1,
PdVector base2,
PdVector normal2)
Compute intersection of plane and plane, and return the intersection line.

lineDir parallel to n1xn2
lineBase = s*n1 + t*n2.

Insert in both plane equations and solve for s and t:
=
=
s + t =
s + t =
=> s = (-)/(1.-**2)
=> t = (-)/(1.-**2)

Method only works in euclidean 3-space.
Parameters:
lineBase - computed point on the intersection line
lineDir - computed direction of the intersection line
base1 - base point of plane1
base2 - base point of plane2
normal1 - unit normal of plane1
normal2 - unit normal of plane2
Returns:
true if both planes intersect
• distOfPointToLine

public static double distOfPointToLine(PdVector p,
PdVector base,
PdVector dir)
Compute distance of point to line. Use formula dist = |(p-base) x dir|.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
p - given point
base - some point of the line
dir - direction of the line with unit length 1.
Returns:
distance of point to line, or Double.MAX_VALUE if line direction not normalized.
• distOfPointToPlane

public static double distOfPointToPlane(PdVector p,
PdVector base,
PdVector normal)
Compute distance of point to plane. Use formula dist = , that means, we use the signed distance which is positive if p lies in direction of the normal.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
p - given point
base - some point of the line
normal - unit normal of plane with length 1.
Returns:
distance signed distance is positive if p is in direction of normal
• distOfLineToLine

public static double distOfLineToLine(PdVector base1,
PdVector dir1,
PdVector base2,
PdVector dir2)
Compute distance of line to line. Use formula dist = ||/|dir1xdir2|. Special care is taken if directions are degenerate.

Currently, method works in Euclidean 3-space only.

Parameters:
base1 - base point of line1
base2 - base point of line2
dir1 - direction of line1
dir2 - direction of line2
Returns:
distance
• projectPointToLine

public static void projectPointToLine(PdVector proj,
PdVector p,
PdVector base,
PdVector dir)
Project a given point to line. Use formula proj = base + dir. Point and projected point may be the same vector instances.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
proj - projection of p to the line
p - given point
base - some point of the line
dir - unit direction of the line
• projectPointToPlane

public static void projectPointToPlane(PdVector proj,
PdVector p,
PdVector base,
PdVector normal)
Project a given point to plane. Use formula p - normal. Point and projected point may be the same vector instances.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
proj - projection of p to the line
p - given point
base - some point of the plane
normal - unit normal of plane
• projectPointToCircle

public static void projectPointToCircle(PdVector proj,
PdVector p,
PdVector mid,
PdVector normal,
Project 3d-point onto circle in 3d by 1) project point onto plane of circle 2) adjust distance to mid point. Point and projected point may be the same vector instances.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
proj - projection of p to the line
p - given point
mid - some point of the plane
normal - unit normal of plane
• projectOntoLine

public static void projectOntoLine(PdVector v,
PdVector dir)
Project a given vector to a line through the origin. Use formula v = dir/|dir|^2.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
v - given vector, also contains the result
dir - unit direction of the line
• projectOntoLine

public static void projectOntoLine(PdVector vProj,
PdVector v,
PdVector dir)
Project a given vector to a line through the origin. Use formula vProj = dir/|dir|^2. Vector and projected vector may be the same vector instances.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
vProj - projection of v to the line through the origin
v - given vector
dir - unit direction of the line
• projectOntoPlane

public static void projectOntoPlane(PdVector v,
PdVector normal)
Project a given vector to a plane through the origin. Use formula v = v-normal/|normal|^2.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
v - given vector, also contains the result
normal - unit normal of the plane
• projectOntoPlane

public static void projectOntoPlane(PdVector vProj,
PdVector v,
PdVector normal)
Project a given vector to a plane through the origin. Use formula vProj = v-normal/|normal|^2. Vector and projected vector may be the same vector instances.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
vProj - projection of v to the plane through the origin
v - given vector
normal - unit normal of the plane
• circleThruPoints

public static boolean circleThruPoints(PdVector center,
PdVector p,
PdVector q,
PdVector r)
Compute circle through three given points. Use formula dist = ||/|dir1xdir2|.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
center - resulting center of circle
p - given point
q - given point
r - given point
Returns:
true if circle could be computed.
• evalCircle

public static boolean evalCircle(PdVector p,
PdVector mid,
PdVector orient,
PdVector start,
PdVector end,
double t)
Compute a point between the two end points of a circle segment. The three points mid, start and end determine the plane of the circle. The vector orient determines the orientation of the circle segment from start to end, i.e. how to run around the circle. The value t specifies the relative position on the segment, t=0 corresponds to start and t=1 corresponds to end.

Method only works in euclidean 3-space.

Parameters:
p - calculated point on circle segment
mid - center of circle
orient - normal vector determines which angle to take
start - first point on circle segment
end - second point on circle segment
t - relative position in [0.,1.] between start and end on segment
Returns:
true if circle could be evaluated.
PdVector.angleWithOrientation(PdVector, PdVector, PdVector), rotatePointAroundLine(PdVector, PdVector, PdVector, PdVector, double)
• evalHelix

public static boolean evalHelix(PdVector p,
PdVector axisBot,
PdVector axisDir,
PdVector start,
PdVector end,
double t)
Compute a point between the two end points of a segment of a helix. The point axisBot and direction axisDir determine an axis which generates a helix when rotating and translating the point start around the axis to the point end. The value t specifies the relative position on the segment, t=0 corresponds to start and t=1 corresponds to end.

Method only works in euclidean 3-space.

Parameters:
p - calculated point on helix segment
axisBot - point on axis of helix
axisDir - unit direction of axis of helix
start - first point on helix
end - second point on helix
t - relative position in [0.,1.] between start and end on segment
Returns:
true if helix could be evaluated.
PdVector.angleWithOrientation(PdVector, PdVector, PdVector), rotatePointAroundLine(PdVector, PdVector, PdVector, PdVector, double)
• rotatePointAroundVector

public static boolean rotatePointAroundVector(PdVector pRot,
PdVector p,
PdVector axisDir,
double alpha)
Rotate a point around an axis through the origin by a given angle.

Method only works in euclidean 3-space.

Parameters:
pRot - rotated point
p - point to rotate. May be equal to pRot.
axisDir - unit direction of rotation axis through origin
alpha - rotation angle, in radians
Returns:
true if rotation could be performed.
rotatePointAroundLine(PdVector,PdVector,PdVector,PdVector,double)
• rotatePointAroundLine

public static boolean rotatePointAroundLine(PdVector pRot,
PdVector p,
PdVector axisBase,
PdVector axisDir,
double alpha)
Rotate a point around an arbitrary axis by a given angle. Axis need not go through the origin.

Method only works in euclidean 3-space.

Parameters:
pRot - rotated point
p - point to rotate
axisBase - some point on the rotation axis
axisDir - unit direction of rotation axis
alpha - rotation angle
Returns:
true if rotation could be performed.
rotatePointAroundVector(PdVector,PdVector,PdVector,double)
• ctg

public static double ctg(PdVector p,
PdVector q1,
PdVector q2)
Compute cotangent of the vertex angle at vertex p in the triangle (p, q1, q2).

Method works in Euclidean vector spaces of arbitrary dimension.

Parameters:
p - vertex where to compute the cotangent
q1 - other vertex of the triangle
q2 - other vertex of the triangle
Returns:
cotangent of vertex angle
ctg(double[],PdVector,PdVector,PdVector)
• sphericalAngle

public static double sphericalAngle(PdVector p,
PdVector q1,
PdVector q2)
Compute spherical angle at vertex p or a triangle on the unit sphere in S^n. All vertices must lie on a unit sphere, i.e. they must have unit length.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
p - vertex where to compute the angle
q1 - other vertex of the triangle
q2 - other vertex of the triangle
Returns:
spherical vertex angle at p
PdVector.angle(PdVector,PdVector,PdVector)
• sphericalArea

public static double sphericalArea(PdVector p,
PdVector q,
PdVector r)
Compute area of a spherical triangle on the unit sphere in S^n. All vertices must lie on a unit sphere, i.e. they must have unit length.

Method works in euclidean vector spaces of arbitrary dimension.

Parameters:
p - vertex of the triangle
q - vertex of the triangle
r - vertex of the triangle
Returns:
area of the spherical triangle
sphericalAngle(PdVector,PdVector,PdVector)
• frameToStandardFrame

public static double[] frameToStandardFrame(PdVector first,
PdVector second,
PdVector third)
Computes the necessary rotations around the y, x and z axis, to transform a given orthonormal frame into the standard basis of R^3. The first vector of the frame is mapped to the x-axis, the second to the y-axis and so on.

So if you want to get these rotation angles for e.g. the camera position, then you should call this method with normalized first = viewdir x upvector, second = upvector and third = -viewdir.

Parameters:
first - First vector of frame -> x-axis. FRAME MUST BE ORTHONORMAL! Orthonormality is not checked by this method!
second - Second vector of frame -> y-axis. See first.
third - Third vector of frame -> z-axis. See first.
Returns:
Array of angles (RAD): angle to rotate around y-axis, around x-axis and around z-axis in this order.