maspack.geometry

Class QuadraticUtils

java.lang.Object

maspack.geometry.QuadraticUtils

public class QuadraticUtils
extends java.lang.Object

Utility methods for quadratic shapes and surfaces.

Field Summary

Fields

Modifier and Type	Field and Description
static double	OUTSIDE Special value, equal to Double.MAX_VALUE, that indicates a point is outside a particular solid.

Constructor Summary

Constructors

Constructor and Description
QuadraticUtils()

Method Summary

Modifier and Type	Method and Description
static int	circleTangentPoints(Point3d t0, Point3d t1, Point3d px, double r) Cpmputes the two tangent points t0 and t1 between a circle of radius r and a point px exterior to it.
static double	ellipsoidPenetrationDistance(Vector3d nrm, Vector3d pos, double a, double b, double c, double amax) Computes the distance from a point to the surface of an ellipsoid, along with the associated normal.
static double	ellipsoidPenetrationDistance(Vector3d nrm, Vector3d pos, double a, double b, double c, double tol, double amax, IntHolder numIters)
static void	ellipsoidSurfaceTangent(Point3d pt, Point3d p0, Point3d p1, double a, double b, double c) Find the point pt for an axis-aligned ellipsoid that is tangent to the line p0-pt and closest to the line defined by p0 and p1.
static boolean	ellipsoidSurfaceTangentInPlane(Point3d pt, Point3d pa, Point3d p0, Vector3d nrm, double a, double b, double c) Find the point pt on an axis-aligned ellipsoid that is tangent to the line pa-pt, lies in the plane defined by p0 and nrm, and is nearest to p0.
static double	nearestPointEllipse(Vector2d p, double a, double b, Vector2d qp) Find the point p on an ellipse closest to a query point qp, and return the corresponding distance.
static double	nearestPointEllipsoid(Vector3d p, double a, double b, double c, Vector3d qp) Find the point p on an ellipsoid closest to qp, and return the corresponding distance.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

OUTSIDE

public static double OUTSIDE

Special value, equal to Double.MAX_VALUE, that indicates a point is outside a particular solid.

Constructor Detail

QuadraticUtils

public QuadraticUtils()

Method Detail

circleTangentPoints

public static int circleTangentPoints(Point3d t0,
                                      Point3d t1,
                                      Point3d px,
                                      double r)

Cpmputes the two tangent points t0 and t1 between a circle of radius r and a point px exterior to it. The circle is assumed to be centered at the origin and lie in the x-y plane, and so the z coordinate of px is ignored. The method returns the number of distinct tangent points, which is normally 2. If px lies on the circle, there is only one tangent (which is equal to px) and the method returns 1. If px lies inside the circle, there are no tangent points, the method returns 0, and t0 and t1 are undefined.

Parameters:

t0 - returns the first tangent point

t1 - returns the second tangent point

px - point for which the tangents should be computed

r - circle radius

Returns:

number of unique tangent points

ellipsoidPenetrationDistance

public static double ellipsoidPenetrationDistance(Vector3d nrm,
                                                  Vector3d pos,
                                                  double a,
                                                  double b,
                                                  double c,
                                                  double amax)

Computes the distance from a point to the surface of an ellipsoid, along with the associated normal. If the point is outside the ellipsoid such that the algebraic distance a defined by

     x^2   y^2   z^2
 a = --- + --- + ---
     a^2   b^2   c^2
 

exceeds amax, the method returns OUTSIDE and the normal is not computed.

ellipsoidPenetrationDistance

public static double ellipsoidPenetrationDistance(Vector3d nrm,
                                                  Vector3d pos,
                                                  double a,
                                                  double b,
                                                  double c,
                                                  double tol,
                                                  double amax,
                                                  IntHolder numIters)

ellipsoidSurfaceTangent

public static void ellipsoidSurfaceTangent(Point3d pt,
                                           Point3d p0,
                                           Point3d p1,
                                           double a,
                                           double b,
                                           double c)

Find the point pt for an axis-aligned ellipsoid that is tangent to the line p0-pt and closest to the line defined by p0 and p1.

ellipsoidSurfaceTangentInPlane

public static boolean ellipsoidSurfaceTangentInPlane(Point3d pt,
                                                     Point3d pa,
                                                     Point3d p0,
                                                     Vector3d nrm,
                                                     double a,
                                                     double b,
                                                     double c)

Find the point pt on an axis-aligned ellipsoid that is tangent to the line pa-pt, lies in the plane defined by p0 and nrm, and is nearest to p0.

The method works by projecting the ellipsoid into either YZ, ZX, or XY planes, depending on which is closest to the plane in question, and then finding the tangent points for the associated ellipse.

nearestPointEllipse

public static double nearestPointEllipse(Vector2d p,
                                         double a,
                                         double b,
                                         Vector2d qp)

Find the point p on an ellipse closest to a query point qp, and return the corresponding distance. The distance is positive if qp is outside the ellipse, and negative if it is inside. Modified from "Distance from a Point to an Ellipse, an Ellipsoidm or a Hyperellipsoid", by David Eberly.

nearestPointEllipsoid

public static double nearestPointEllipsoid(Vector3d p,
                                           double a,
                                           double b,
                                           double c,
                                           Vector3d qp)

Find the point p on an ellipsoid closest to qp, and return the corresponding distance. The distance is positive if qp is outside the ellipsoid, and negative if it is inside. Modified from "Distance from a Point to an Ellipse, an Ellipsoidm or a Hyperellipsoid", by David Eberly.