Module org.bzdev.graphics

Package org.bzdev.geom

Class Path3DInfo.SegmentData

java.lang.Object

org.bzdev.geom.Path3DInfo.SegmentData

Enclosing class:

Path3DInfo

public static final class Path3DInfo.SegmentData
extends Object

Class to store values used in computations on a segment of a path.

Constructor Summary

Constructors

Constructor	Description
SegmentData(int st, double x0, double y0, double z0, double[] coords, Path3DInfo.SegmentData last)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	curvature(Path3DInfo.UValues uv)	Compute the curvature at a point with a given path parameter If the path segment's type of SEG_CLOSE and the starting and ending points of the segment are identical, the curvature at the end of the previous segment is returned.
boolean	curvatureExists(Path3DInfo.UValues uv)	Determine if the curvature exists for the specified argument.
double	d2sDu2(Path3DInfo.UValues uv)	Compute the second derivative with respect to the path parameter of the signed distance along the path from its initial point
double	d2xDu2(Path3DInfo.UValues uv)	Compute the second derivative with respect to the path parameter of the x coordinate of a point on the path.
double	d2yDu2(Path3DInfo.UValues uv)	Compute the second derivative with respect to the path parameter of the y coordinate of a point on the path.
double	d2zDu2(Path3DInfo.UValues uv)	Compute the second derivative with respect to the path parameter of the z coordinate of a point on the path.
double	d3xDu3(Path3DInfo.UValues uv)	Compute the third derivative with respect to the path parameter of the x coordinate of a point on the path.
double	d3yDu3(Path3DInfo.UValues uv)	Compute the third derivative with respect to the path parameter of the y coordinate of a point on the path.
double	d3zDu3(Path3DInfo.UValues uv)	Compute the third derivative with respect to the path parameter of the z coordinate of a point on the path.
double	dsDu(Path3DInfo.UValues uv)	Compute the derivative with respect to the path parameter of the signed distance along the path from its initial point
double	dxDu(Path3DInfo.UValues uv)	Compute the derivative with respect to the path parameter of the x coordinate of a point on the path.
double	dyDu(Path3DInfo.UValues uv)	Compute the derivative with respect to the path parameter of the y coordinate of a point on the path.
double	dzDu(Path3DInfo.UValues uv)	Compute the derivative with respect to the path parameter of the z coordinate of a point on the path.
boolean	getBinormal(Path3DInfo.UValues uv, double[] array, int offset)	Get the binormal vector for a given value of the path parameter and an offset for the array storing the normal vector.
boolean	getNormal(Path3DInfo.UValues uv, double[] array, int offset)	Get the normal vector for a given value of the path parameter and an offset for the array storing the normal vector.
boolean	getTangent(Path3DInfo.UValues uv, double[] array, int offset)	Get the tangent vector for a specified value of the path parameter and an output-array offset.
double	getX(Path3DInfo.UValues uv)	Compute the x coordinate of a point on the path.
double	getY(Path3DInfo.UValues uv)	Compute the x coordinate of a point on the path.
double	getZ(Path3DInfo.UValues uv)	Compute the x coordinate of a point on the path.
double	torsion(Path3DInfo.UValues uv)	Compute the torsion at a point with a given path parameter If the path segment's type of SEG_CLOSE and the starting and ending points of the segment are identical, the torsion at the end of the previous segment is returned.

Methods inherited from class java.lang.Object

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

Constructor Details

SegmentData

public SegmentData(int st,
 double x0,
 double y0,
 double z0,
 double[] coords,
 Path3DInfo.SegmentData last)
            throws IllegalArgumentException

Constructor.

Parameters:

st - the path-segment type, legal values of which are

• PathIterator3D.SEG_MOVETO
• PathIterator3D.SEG_LINETO
• PathIterator3D.SEG_QUADTO
• PathIterator3D.SEG_CUBICTO
• PathIterator3D.SEG_CLOSE

x0 - the initial x coordinate for the segment (ignored for the PathIterator3D.SEG_MOVETO case)

y0 - the initial y coordinate for the segment (ignored for the PathIterator3D.SEG_MOVETO case)

z0 - the initial y coordinate for the segment (ignored for the PathIterator3D.SEG_MOVETO case)

coords - the coordinates array set by a call to PathIterator3D.currentSegment(double[]), but with the first three elements set to the x, y, and z coordinates respectively for the previous PathIterator3D.SEG_MOVETO segment when first argument's value is PathIterator3D.SEG_CLOSE. The size of this array should be at least 3 and the maximum size needed is 9.

last - the previous SegmentData for a path; null if there is none

Throws:

IllegalArgumentException - a value was out of range

ArrayIndexOutOfBoundsException - the array argument was two small

NullPointerException - the array argument was null

See Also:

• PathIterator3D

Method Details

getX

public double getX(Path3DInfo.UValues uv)

Compute the x coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the x coordinate

getY

public double getY(Path3DInfo.UValues uv)

Compute the x coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the y coordinate

getZ

public double getZ(Path3DInfo.UValues uv)

Compute the x coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the y coordinate

dxDu

public double dxDu(Path3DInfo.UValues uv)

Compute the derivative with respect to the path parameter of the x coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the derivative of the x coordinate with respect to the path parameter

dyDu

public double dyDu(Path3DInfo.UValues uv)

Compute the derivative with respect to the path parameter of the y coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the derivative of the y coordinate with respect to the path parameter

dzDu

public double dzDu(Path3DInfo.UValues uv)

Compute the derivative with respect to the path parameter of the z coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the derivative of the y coordinate with respect to the path parameter

d2xDu2

public double d2xDu2(Path3DInfo.UValues uv)

Compute the second derivative with respect to the path parameter of the x coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the second derivative of the x coordinate with respect to the path parameter

d2yDu2

public double d2yDu2(Path3DInfo.UValues uv)

Compute the second derivative with respect to the path parameter of the y coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the second derivative of the y coordinate with respect to the path parameter

d2zDu2

public double d2zDu2(Path3DInfo.UValues uv)

Compute the second derivative with respect to the path parameter of the z coordinate of a point on the path.

Parameters:

uv - the path parameter

Returns:

the second derivative of the y coordinate with respect to the path parameter

d3xDu3

public double d3xDu3(Path3DInfo.UValues uv)

Compute the third derivative with respect to the path parameter of the x coordinate of a point on the path.

Note: the value is 0.0 except for cubic segments, where the value is a constant.

Parameters:

uv - the path parameter

Returns:

the third derivative of the x coordinate with respect to the path parameter

d3yDu3

public double d3yDu3(Path3DInfo.UValues uv)

Compute the third derivative with respect to the path parameter of the y coordinate of a point on the path.

Note: the value is 0.0 except for cubic segments, where the value is a constant.

Parameters:

uv - the path parameter

Returns:

the third derivative of the y coordinate with respect to the path parameter

d3zDu3

public double d3zDu3(Path3DInfo.UValues uv)

Compute the third derivative with respect to the path parameter of the z coordinate of a point on the path.

Note: the value is 0.0 except for cubic segments, where the value is a constant.

Parameters:

uv - the path parameter

Returns:

the third derivative of the y coordinate with respect to the path parameter

dsDu

public double dsDu(Path3DInfo.UValues uv)

Compute the derivative with respect to the path parameter of the signed distance along the path from its initial point

Parameters:

uv - the path parameter

Returns:

the derivative of the signed distance along the path with respect to the path parameter

d2sDu2

public double d2sDu2(Path3DInfo.UValues uv)

Compute the second derivative with respect to the path parameter of the signed distance along the path from its initial point

Parameters:

uv - the path parameter

Returns:

the second derivative of the signed distance along the path with respect to the path parameter

curvature

public double curvature(Path3DInfo.UValues uv)

Compute the curvature at a point with a given path parameter If the path segment's type of SEG_CLOSE and the starting and ending points of the segment are identical, the curvature at the end of the previous segment is returned.

Parameters:

uv - the path parameter

Returns:

the curvature

torsion

public double torsion(Path3DInfo.UValues uv)

Compute the torsion at a point with a given path parameter If the path segment's type of SEG_CLOSE and the starting and ending points of the segment are identical, the torsion at the end of the previous segment is returned.

Parameters:

uv - the path parameter

Returns:

the torsion

curvatureExists

public boolean curvatureExists(Path3DInfo.UValues uv)

Determine if the curvature exists for the specified argument. In general, the curvature does not exist when all the points along a segment are the same point or when the segment is a SEG_MOVETO segment (which just indicates the start of a curve). For a SEG_CLOSE segment where the starting and ending points are identical, the curvature exists if the curvature of the previous segment exists at its end (u = 1.0).

Parameters:

uv - the path parameter

Returns:

true if the curvature exists; false otherwise

getTangent

public boolean getTangent(Path3DInfo.UValues uv,
 double[] array,
 int offset)

Get the tangent vector for a specified value of the path parameter and an output-array offset. If the tangent vector does not exist (e.g., the length of the line does not vary with the path parameter), the tangent vector will be set to zero. The tangent vector will have unit length if it is not zero.

Parameters:

uv - the path parameter

array - an array of length no less than 3 used to store the tangent vector, with array[offset] containing the tangent vector's X component, array[offset+1] containing the tangent vector's Y component, and array[offset+2] containing the tangent vector's Z component

offset - the index into the array at which to store the tangent vector

Returns:

true if the tangent vector exists; false if the tangent vector does not exist

getNormal

public boolean getNormal(Path3DInfo.UValues uv,
 double[] array,
 int offset)

Get the normal vector for a given value of the path parameter and an offset for the array storing the normal vector. The normal vector N is a vector of unit length, perpendicular to the tangent vector, and oriented so that d²r/ds² = κN where κ is the curvature. If the normal vector does not exist (e.g., the length of the line does not vary with the path parameter), the normal vector will not be changed.

Parameters:

uv - the path parameter

array - an array of length no less than 3 used to store the normal vector, with array[offset] containing the normal vector's X component, array[offset+1] containing the normal vector's Y component, and array[offset+2] containing the normal vector's Z component

offset - the index into the array at which to store the normal vector

Returns:

true if the normal vector exists; false if the normal vector does not exist

getBinormal

public boolean getBinormal(Path3DInfo.UValues uv,
 double[] array,
 int offset)

Get the binormal vector for a given value of the path parameter and an offset for the array storing the normal vector. The binormal vector is defined as the cross product T × N of the tangent and normal vectors. If the binormal vector does not exist (e.g., the length of the line does not vary with the path parameter or the path is locally straight), the binormal vector will be set to zero.

Parameters:

uv - the path parameter

array - an array of length no less than 3 used to store the normal vector, with array[offset] containing the normal vector's X component, array[offset+1] containing the normal vector's Y component, and array[offset+2] containing the normal vector's Z component

offset - the index into the array at which to store the normal vector

Returns:

true if the binormal vector exists; false if the normal vector does not exist