PuVectorGeom ("JavaView Reference Manual")

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 Summary

Constructors
Constructor and Description

PuVectorGeom()

Constructors
Constructor and Description
`PuVectorGeom()`

Method Summary

Methods
Modifier and Type	Method and Description
`static boolean`	`circleThruPoints(PdVector center, double radius, PdVector p, PdVector q, PdVector r)` Compute circle through three given points.
`static void`	`ctg(double[] ctg, PdVector p, PdVector q, PdVector r)` Compute cotangent of the vertex angles at all vertices of the triangle (p, q, r).
`static double`	`ctg(PdVector p, PdVector q1, PdVector q2)` Compute cotangent of the vertex angle at vertex p in the triangle (p, q1, q2).
`static double`	`distOfLineToLine(PdVector base1, PdVector dir1, PdVector base2, PdVector dir2)` Compute distance of line to line.
`static double`	`distOfPointToLine(PdVector p, PdVector base, PdVector dir)` Compute distance of point to line.
`static double`	`distOfPointToPlane(PdVector p, PdVector base, PdVector normal)` Compute distance of point to plane.
`static double`	`distVectorOfLineToLine(PdVector lot, PdVector base1, PdVector dir1, PdVector base2, PdVector dir2)` Compute shortest distance vector of line to line.
`static void`	`distVectorOfPointToLine(PdVector lot, PdVector p, PdVector base, PdVector dir)` Compute shortest distance vector of point to line.
`static void`	`distVectorOfPointToPlane(PdVector lot, PdVector p, PdVector base, PdVector normal)` Compute shortest distance vector of point to plane.
`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.
`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.
`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.
`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`.
`static double`	`intersectionOfLineAndPlane(PdVector p, PdVector base1, PdVector dir, PdVector base2, PdVector normal)` Compute intersection line and plane.
`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.
`static void`	`projectOntoLine(PdVector v, PdVector dir)` Project a given vector to a line through the origin.
`static void`	`projectOntoLine(PdVector vProj, PdVector v, PdVector dir)` Project a given vector to a line through the origin.
`static void`	`projectOntoPlane(PdVector v, PdVector normal)` Project a given vector to a plane through the origin.
`static void`	`projectOntoPlane(PdVector vProj, PdVector v, PdVector normal)` Project a given vector to a plane through the origin.
`static void`	`projectPointToCircle(PdVector proj, PdVector p, PdVector mid, PdVector normal, double radius)` Project 3d-point onto circle in 3d by 1) project point onto plane of circle 2) adjust distance to mid point.
`static void`	`projectPointToLine(PdVector proj, PdVector p, PdVector base, PdVector dir)` Project a given point to line.
`static void`	`projectPointToPlane(PdVector proj, PdVector p, PdVector base, PdVector normal)` Project a given point to plane.
`static boolean`	`rotatePointAroundLine(PdVector pRot, PdVector p, PdVector axisBase, PdVector axisDir, double alpha)` Rotate a point around an arbitrary axis by a given angle.
`static boolean`	`rotatePointAroundVector(PdVector pRot, PdVector p, PdVector axisDir, double alpha)` Rotate a point around an axis through the origin by a given angle.
`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.
`static double`	`sphericalArea(PdVector p, PdVector q, PdVector r)` Compute area of a spherical triangle on the unit sphere in S^n.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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
  - distVectorOfPointToLine
```
public static void distVectorOfPointToLine(PdVector lot,
                           PdVector p,
                           PdVector base,
                           PdVector dir)
```
    Compute shortest distance vector of point to line.
    Method works in euclidean vector spaces of arbitrary dimension.
    
    Parameters:
    lot - resulting distance vector
    p - given point
    base - some point of the line
    dir - unit direction of the line
    See Also:
    projectPointToLine(jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector)
  - distVectorOfPointToPlane
```
public static void distVectorOfPointToPlane(PdVector lot,
                            PdVector p,
                            PdVector base,
                            PdVector normal)
```
    Compute shortest distance vector of point to plane.
    Method works in euclidean vector spaces of arbitrary dimension.
    
    Parameters:
    lot - resulting distance vector
    p - given point
    base - some point on the plane
    normal - unit normal of plane
    See Also:
    projectPointToPlane(jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector)
  - distVectorOfLineToLine
```
public static double distVectorOfLineToLine(PdVector lot,
                            PdVector base1,
                            PdVector dir1,
                            PdVector base2,
                            PdVector dir2)
```
    Compute shortest distance vector of line to line. Method only works in euclidean 3-spaces.
    
    Parameters:
    lot - resulting distance vector
    base1 - base point of line1
    base2 - base point of line2
    dir1 - direction of line1
    dir2 - direction of line2
    
    Returns:
    distance of both lines, or Double.MAX_VALUE if parallel.
    See Also:
    distOfLineToLine(jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector, jv.vecmath.PdVector)
  - 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,
                        double radius)
```
    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,
                       double radius,
                       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
    radius - resulting radius 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.
    See Also:
    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.
    See Also:
    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.
    See Also:
    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.
    See Also:
    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
    See Also:
    ctg(double[],PdVector,PdVector,PdVector)
  - ctg
```
public static void ctg(double[] ctg,
       PdVector p,
       PdVector q,
       PdVector r)
```
    Compute cotangent of the vertex angles at all vertices of the triangle (p, q, r).
    Method works in Euclidean vector spaces of arbitrary dimension.
    
    Parameters:
    ctg - cotangent of all vertex angles
    p - vertex of the triangle
    q - vertex of the triangle
    r - vertex of the triangle
    See Also:
    ctg(PdVector,PdVector,PdVector), PuMath.ctg(double[],double,double,double)
  - 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
    See Also:
    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
    See Also:
    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.

Class PuVectorGeom

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PuVectorGeom

Method Detail

intersectionOfLineAndLine

intersectionOfLineAndPlane

intersectionOfPlaneAndPlane

distVectorOfPointToLine

distVectorOfPointToPlane

distVectorOfLineToLine

distOfPointToLine

distOfPointToPlane

distOfLineToLine

projectPointToLine

projectPointToPlane

projectPointToCircle

projectOntoLine

projectOntoLine

projectOntoPlane

projectOntoPlane

circleThruPoints

evalCircle

evalHelix

rotatePointAroundVector

rotatePointAroundLine

ctg

ctg

sphericalAngle

sphericalArea

frameToStandardFrame