java.lang.Object
- geomss.geom.AbstractGeomElement<T>
- - geomss.geom.AbstractSurface<T>

Type Parameters:

T - The sub-type of this AbstractSurface element.

All Implemented Interfaces:

GeomElement<T>, ParametricGeometry<T>, Surface<T>, Transformable<T>, java.io.Serializable, java.lang.Cloneable, java.lang.Comparable, javolution.lang.Reusable, javolution.xml.XMLSerializable

Direct Known Subclasses:

LoftedSurface, NurbsSurface, SubrangeSurface, TFISurface
```
public abstract class AbstractSurface<T extends AbstractSurface>
extends AbstractGeomElement<T>
implements Surface<T>
```
The interface and implementation in common to all surfaces.
Modified by: Joseph A. Huwaldt

Version:

February 14, 2025

Author:

Joseph A. Huwaldt, Date: June 14, 2010

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field Description

static double GTOL
Generic/default tolerance for use in root finders, etc.
- Fields inherited from class geomss.geom.AbstractGeomElement
  RESOURCES

Constructor Summary

Constructors
Constructor Description

AbstractSurface()

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method	Description
`PointArray<SubrangePoint>`	`extractGrid(GridRule gridRule, java.util.List<java.lang.Double> bottomSpacing, java.util.List<java.lang.Double> topSpacing, java.util.List<java.lang.Double> leftSpacing, java.util.List<java.lang.Double> rightSpacing)`	Return an array of SubrangePoint objects that are gridded onto the surface using the specified spacings and gridding rule.
`Parameter<javax.measure.quantity.Area>`	`getArea(double eps)`	Return the surface area of this entire surface.
`Parameter<javax.measure.quantity.Area>`	`getArea(double s1, double t1, double s2, double t2, double eps)`	Return the surface area of a portion of this surface.
`Parameter<javax.measure.quantity.Area>`	`getArea(GeomPoint st1, GeomPoint st2, double eps)`	Return the surface area of a portion of this surface.
`PointString<SubrangePoint>`	`getClosest(Curve curve, double tol)`	Returns the closest points (giving the minimum distance) between this surface and the specified curve.
`SubrangePoint`	`getClosest(GeomPlane plane, double tol)`	Returns the closest point (giving the minimum distance) between this surface and the specified plane.
`SubrangePoint`	`getClosest(GeomPoint point, double tol)`	Returns the closest point on this surface to the specified point.
`SubrangePoint`	`getClosest(GeomPoint point, double nearS, double nearT, double tol)`	Returns the closest point on this surface to the specified point near the specified parametric position.
`PointString<SubrangePoint>`	`getClosest(Surface surface, double tol)`	Returns the closest points (giving the minimum distance) between this surface and the specified surface.
`PointArray<SubrangePoint>`	`getClosest(java.util.List<? extends java.util.List<GeomPoint>> points, double tol)`	Returns the array of closest points on this surface to the specified array (list of lists) of points.
`SubrangeCurve`	`getCurve(Curve pcrv)`	Return a subrange curve on the surface for the given parametric position curve.
`java.util.List<java.util.List<Vector<javax.measure.quantity.Length>>>`	`getDerivatives(GeomPoint st, int grade)`	Calculate all the derivatives from `0` to `grade` with respect to parametric position(s) on a parametric object for the given parametric position on the object, `d^{grade}p(s)/d^{grade}s`.
`SubrangePoint`	`getFarthest(GeomPoint point, double tol)`	Returns the farthest point on this surface from the specified point.
`SubrangePoint`	`getFarthest(GeomPoint point, double nearS, double nearT, double tol)`	Returns the farthest point on this surface from the specified point near the specified parametric position on the surface.
`PointArray<SubrangePoint>`	`getFarthest(java.util.List<? extends java.util.List<GeomPoint>> points, double tol)`	Returns the array of farthest points on this surface from the specified array (list of lists) of points.
`Parameter`	`getGaussianCurvature(double s, double t)`	Returns the Gaussian Curvature for this surface at the given parametric position (s,t) on this surface.
`Parameter`	`getGaussianCurvature(GeomPoint st)`	Returns the Gaussian Curvature for this surface at the given parametric position (s,t) on this surface.
`SubrangePoint`	`getLimitPoint(int dim, boolean max, double tol)`	Returns the most extreme point, either minimum or maximum, in the specified coordinate direction on this surface.
`Parameter`	`getMeanCurvature(double s, double t)`	Returns the Mean Curvature for this surface at the given parametric position (s,t) on this surface.
`Parameter`	`getMeanCurvature(GeomPoint st)`	Returns the Mean Curvature for this surface at the given parametric position (s,t) on this surface.
`Vector<javax.measure.quantity.Dimensionless>`	`getNormal(double s, double t)`	Return the at least 3D normal vector for this surface at the given parametric position (s,t) on this surface.
`Vector<javax.measure.quantity.Dimensionless>`	`getNormal(GeomPoint st)`	Return the normal vector for this surface at the given parametric position (s,t) on this surface.
`int`	`getParDimension()`	Returns the number of parametric dimensions of the geometry element.
`SubrangePoint`	`getPoint(double s, double t)`	Return a subrange point on the surface for the given parametric position on the surface.
`SubrangePoint`	`getPoint(GeomPoint st)`	Return a subrange point on the surface for the given parametric position on the surface.
`Point`	`getRealPoint(GeomPoint st)`	Calculate a point on the surface for the given parametric position on the surface.
`SubrangeCurve`	`getSCurve(double s)`	Return a subrange curve at a constant parametric s-value.
`Vector<javax.measure.quantity.Length>`	`getSDerivative(double s, double t, int grade)`	Calculate a derivative with respect to parametric s-distance of the given grade on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}s`.
`Vector<javax.measure.quantity.Length>`	`getSDerivative(GeomPoint st, int grade)`	Calculate a derivative with respect to parametric s-distance of the given grade on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}s`.
`java.util.List<Vector<javax.measure.quantity.Length>>`	`getSDerivatives(double s, double t, int grade)`	Calculate all the derivatives from `0` to `grade` with respect to parametric s-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}s`.
`abstract java.util.List<Vector<javax.measure.quantity.Length>>`	`getSDerivatives(double s, double t, int grade, boolean scaled)`	Calculate all the derivatives from `0` to `grade` with respect to parametric s-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}s`.
`java.util.List<Vector<javax.measure.quantity.Length>>`	`getSDerivatives(GeomPoint st, int grade)`	Calculate all the derivatives from `0` to `grade` with respect to parametric s-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}s`.
`Plane`	`getTangentPlane(double s, double t)`	Return the tangent plane to this surface at the given parametric position (s,t) on this surface.
`Plane`	`getTangentPlane(GeomPoint st)`	Return the tangent plane to this surface at the given parametric position (s,t) on this surface.
`SubrangeCurve`	`getTCurve(double t)`	Return a subrange curve at a constant parametric t-value.
`Vector<javax.measure.quantity.Length>`	`getTDerivative(double s, double t, int grade)`	Calculate a derivative with respect to parametric t-distance of the given grade on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}t`.
`Vector<javax.measure.quantity.Length>`	`getTDerivative(GeomPoint st, int grade)`	Calculate a derivative with respect to parametric t-distance of the given grade on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}t`.
`java.util.List<Vector<javax.measure.quantity.Length>>`	`getTDerivatives(double s, double t, int grade)`	Calculate all the derivatives from `0` to `grade` with respect to parametric t-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}t`.
`abstract java.util.List<Vector<javax.measure.quantity.Length>>`	`getTDerivatives(double s, double t, int grade, boolean scaled)`	Calculate all the derivatives from `0` to `grade` with respect to parametric t-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}t`.
`java.util.List<Vector<javax.measure.quantity.Length>>`	`getTDerivatives(GeomPoint st, int grade)`	Calculate all the derivatives from `0` to `grade` with respect to parametric t-position on the surface for the given parametric position on the surface, `d^{grade}p(s,t)/d^{grade}t`.
`Vector<javax.measure.quantity.Length>`	`getTwistVector(GeomPoint st)`	Calculate the twist vector (d^2P/(ds*dt) = d(dP/ds)/dt) for this surface at the specified position on this surface.
`Parameter<javax.measure.quantity.Volume>`	`getVolume(double eps)`	Return the enclosed volume of this entire surface.
`Parameter<javax.measure.quantity.Volume>`	`getVolume(double s1, double t1, double s2, double t2, double eps)`	Return the enclosed volume of a portion of this surface.
`Parameter<javax.measure.quantity.Volume>`	`getVolume(GeomPoint st1, GeomPoint st2, double eps)`	Return the enclosed volume of a portion of this surface.
`PointArray<SubrangePoint>`	`gridToTolerance(Parameter<javax.measure.quantity.Length> tol)`	Return an array of points that are gridded onto the surface with the number of points and spacing chosen to result in straight line segments between the points that have mid-points that are all within the specified tolerance of this surface.
`GeomList<PointString<SubrangePoint>>`	`intersect(Curve curve, Parameter<javax.measure.quantity.Length> tol)`	Return the intersections between a curve and this surface.
`GeomList<SubrangeCurve>`	`intersect(GeomPlane plane, Parameter<javax.measure.quantity.Length> tol)`	Return the intersections between an infinite plane and this surface.
`PointString<SubrangePoint>`	`intersect(GeomPoint L0, GeomVector Ldir, Parameter<javax.measure.quantity.Length> tol)`	Return the intersections between an infinite line and this surface.
`GeomList<PointString<SubrangePoint>>`	`intersect(LineSegment line, Parameter<javax.measure.quantity.Length> tol)`	Return the intersections between a line segment and this surface.
`GeomList<GeomList<SubrangeCurve>>`	`intersect(Surface surface, Parameter<javax.measure.quantity.Length> tol)`	Return the intersections between another surface and this surface.
`boolean`	`isDegenerate(Parameter<javax.measure.quantity.Length> tol)`	Return `true` if this surface is degenerate (i.e.: has area less than the specified tolerance squared).
`boolean`	`isPlanar(double epsFT, double epsELT)`	Return `true` if this surface is planar or `false` if it is not.
`boolean`	`isPlanar(Parameter<javax.measure.quantity.Length> tol)`	Return `true` if this surface is planar or `false` if it is not.
`GeomList<T>`	`splitAtS(GeomPoint st)`	Split this surface at the specified parametric S-position returning a list containing two new surfaces (a lower surface with smaller S-parametric positions than "s" and an upper surface with larger S-parametric positions).
`GeomList<T>`	`splitAtT(GeomPoint st)`	Split this surface at the specified parametric T-position returning a list containing two new surfaces (a lower surface with smaller T-parametric positions than "t" and an upper surface with larger T-parametric positions).
`T`	`transpose()`	Always throws UnsupportedOperationException as this method is not supported for this object type! Subclasses that do support transpose() should override this method.

Methods inherited from class geomss.geom.AbstractGeomElement
addChangeListener, clone, compareTo, equals, getAllUserData, getID, getName, getUserData, hashCode, putAllUserData, putUserData, removeChangeListener, removeUserData, reset, setName, toString, toText

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

Methods inherited from interface java.lang.Comparable
compareTo

Methods inherited from interface geomss.geom.GeomElement
addChangeListener, copyToReal, getAllUserData, getBoundsMax, getBoundsMin, getID, getName, getPhyDimension, getUnit, getUserData, isValid, putAllUserData, putUserData, removeChangeListener, removeUserData, setName, size, toText

Methods inherited from interface geomss.geom.Surface
copy, getRealPoint, getS0Curve, getS1Curve, getT0Curve, getT1Curve, getTwistVector, reverseS, reverseT, splitAtS, splitAtT, to, toDimension, toNurbs

Methods inherited from interface geomss.geom.Transformable
getTransformed

- Field Detail
  - GTOL
```
public static final double GTOL
```
    Generic/default tolerance for use in root finders, etc.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - AbstractSurface
```
public AbstractSurface()
```
- Method Detail
  - getParDimension
```
public int getParDimension()
```
    Returns the number of parametric dimensions of the geometry element. This implementation always returns 2.
    
    Specified by:
    
    getParDimension in interface GeomElement<T extends AbstractSurface>
    
    Returns:
    
    The number of parametric dimensions of this geometry element.
  - transpose
```
public T transpose()
```
    Always throws UnsupportedOperationException as this method is not supported for this object type! Subclasses that do support transpose() should override this method.
    
    Specified by:
    
    transpose in interface Surface<T extends AbstractSurface>
    
    Returns:
    
    A new surface, identical to this one, but with the transpose of the parameterization.
    
    Throws:
    
    java.lang.UnsupportedOperationException - as this method is not supported on this object type.
  - splitAtS
```
public GeomList<T> splitAtS(GeomPoint st)
```
    Split this surface at the specified parametric S-position returning a list containing two new surfaces (a lower surface with smaller S-parametric positions than "s" and an upper surface with larger S-parametric positions).
    
    Specified by:
    
    splitAtS in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The S-parametric position where this surface should be split (must not be 0 or 1!). Must be a 2-dimensional point with each value in the range 0 to 1, only the 1st value is used. Units are ignored. May not be null.
    
    Returns:
    
    A list containing two surfaces: 0 == the lower surface, 1 == the upper surface.
  - splitAtT
```
public GeomList<T> splitAtT(GeomPoint st)
```
    Split this surface at the specified parametric T-position returning a list containing two new surfaces (a lower surface with smaller T-parametric positions than "t" and an upper surface with larger T-parametric positions).
    
    Specified by:
    
    splitAtT in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The T-parametric position where this surface should be split (must not be 0 or 1!). Must be a 2-dimensional point with each value in the range 0 to 1, only the 2nd value is used. Units are ignored. May not be null.
    
    Returns:
    
    A list containing two surfaces: 0 == the lower surface, 1 == the upper surface.
  - getPoint
```
public SubrangePoint getPoint(double s,
                              double t)
```
    Return a subrange point on the surface for the given parametric position on the surface.
    
    Specified by:
    
    getPoint in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate a point for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate a point for (0.0 to 1.0 inclusive).
    
    Returns:
    
    The subrange point on the surface at the specified parameter values.
    
    Throws:
    
    java.lang.IllegalArgumentException - if there is any problem with the parameter values.
  - getPoint
```
public SubrangePoint getPoint(GeomPoint st)
```
    Return a subrange point on the surface for the given parametric position on the surface.
    
    Specified by:
    
    getPoint in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    getPoint in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate a point for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The subrange point on the surface at the specified parameter values.
    
    Throws:
    
    java.lang.IllegalArgumentException - if there is any problem with the parameter values.
  - getRealPoint
```
public Point getRealPoint(GeomPoint st)
```
    Calculate a point on the surface for the given parametric position on the surface.
    
    Specified by:
    
    getRealPoint in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    getRealPoint in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate a point for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The calculated point on the surface at the specified parameter values.
    
    Throws:
    
    java.lang.IllegalArgumentException - if there is any problem with the parameter values.
  - getCurve
```
public SubrangeCurve getCurve(Curve pcrv)
```
    Return a subrange curve on the surface for the given parametric position curve.
    
    Specified by:
    
    getCurve in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    pcrv - A curve in parametric space indicating the parametric positions on the the surface represented by the subrange curve. Must be 2D with values between 0 and 1.
    
    Returns:
    
    The subrange curve on the surface at the specified parametric curve positions.
  - getSCurve
```
public SubrangeCurve getSCurve(double s)
```
    Return a subrange curve at a constant parametric s-value.
    
    Specified by:
    
    getSCurve in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - The parametric s-position to extract a subrange curve.
    
    Returns:
    
    The subrange curve on the surface at the specified s-value.
    
    Throws:
    
    java.lang.IllegalArgumentException - if there is any problem with the parameter value.
  - getTCurve
```
public SubrangeCurve getTCurve(double t)
```
    Return a subrange curve at a constant parametric t-value.
    
    Specified by:
    
    getTCurve in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    t - The parametric t-position to extract a subrange curve.
    
    Returns:
    
    The subrange curve on the surface at the specified t-value.
    
    Throws:
    
    java.lang.IllegalArgumentException - if there is any problem with the parameter value.
  - getDerivatives
```
public java.util.List<java.util.List<Vector<javax.measure.quantity.Length>>> getDerivatives(GeomPoint st,
                                                                                            int grade)
```
    Calculate all the derivatives from 0 to grade with respect to parametric position(s) on a parametric object for the given parametric position on the object, d^{grade}p(s)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns [p(s), dp(s)/ds];
    2nd derivative (grade = 2), this returns [p(s), dp(s)/ds, d^2p(s)/d^2s]; etc.
    
    Specified by:
    
    getDerivatives in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    getDerivatives in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the derivatives for. Must match the parametric dimension of this parametric surface and have each value in the range 0 to 1.0. Units are ignored.
    
    grade - The maximum grade to calculate the derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    A list of lists of derivatives (one list for each parametric dimension). Each list contains derivatives up to the specified grade at the specified parametric position. Example: for a surface list element 0 is the array of derivatives in the 1st parametric dimension (s), then 2nd list element is the array of derivatives in the 2nd parametric dimension (t).
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getSDerivatives
```
public java.util.List<Vector<javax.measure.quantity.Length>> getSDerivatives(GeomPoint st,
                                                                             int grade)
```
    Calculate all the derivatives from 0 to grade with respect to parametric s-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/ds];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/ds, d^2p(s,t)/d^2s]; etc.
    
    Specified by:
    
    getSDerivatives in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the derivatives for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    grade - The maximum grade to calculate the derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    A list of s-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getSDerivatives
```
public java.util.List<Vector<javax.measure.quantity.Length>> getSDerivatives(double s,
                                                                             double t,
                                                                             int grade)
```
    Calculate all the derivatives from 0 to grade with respect to parametric s-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/ds];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/ds, d^2p(s,t)/d^2s]; etc.
    
    Specified by:
    
    getSDerivatives in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The maximum grade to calculate the u-derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    A list of s-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getSDerivatives
```
public abstract java.util.List<Vector<javax.measure.quantity.Length>> getSDerivatives(double s,
                                                                                      double t,
                                                                                      int grade,
                                                                                      boolean scaled)
```
    Calculate all the derivatives from 0 to grade with respect to parametric s-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/ds];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/ds, d^2p(s,t)/d^2s]; etc.
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The maximum grade to calculate the u-derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    scaled - Pass true for properly scaled derivatives or false if the magnitude of the derivative vector is not required -- this sometimes results in faster calculation times.
    
    Returns:
    
    A list of s-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTDerivatives
```
public java.util.List<Vector<javax.measure.quantity.Length>> getTDerivatives(GeomPoint st,
                                                                             int grade)
```
    Calculate all the derivatives from 0 to grade with respect to parametric t-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}t.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/dt];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/dt, d^2p(s,t)/d^2t]; etc.
    
    Specified by:
    
    getTDerivatives in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the derivatives for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    grade - The maximum grade to calculate the derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    A list of t-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTDerivatives
```
public java.util.List<Vector<javax.measure.quantity.Length>> getTDerivatives(double s,
                                                                             double t,
                                                                             int grade)
```
    Calculate all the derivatives from 0 to grade with respect to parametric t-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}t.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/dt];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/dt, d^2p(s,t)/d^2t]; etc.
    
    Specified by:
    
    getTDerivatives in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The maximum grade to calculate the v-derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    A list of t-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTDerivatives
```
public abstract java.util.List<Vector<javax.measure.quantity.Length>> getTDerivatives(double s,
                                                                                      double t,
                                                                                      int grade,
                                                                                      boolean scaled)
```
    Calculate all the derivatives from 0 to grade with respect to parametric t-position on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}t.
    Example:
    1st derivative (grade = 1), this returns [p(s,t), dp(s,t)/dt];
    2nd derivative (grade = 2), this returns [p(s,t), dp(s,t)/dt, d^2p(s,t)/d^2t]; etc.
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The maximum grade to calculate the v-derivatives for (1=1st derivative, 2=2nd derivative, etc)
    
    scaled - Pass true for properly scaled derivatives or false if the magnitude of the derivative vector is not required -- this sometimes results in faster calculation times.
    
    Returns:
    
    A list of t-derivatives up to the specified grade of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getSDerivative
```
public Vector<javax.measure.quantity.Length> getSDerivative(GeomPoint st,
                                                            int grade)
```
    Calculate a derivative with respect to parametric s-distance of the given grade on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns dp(s,t)/ds;
    2nd derivative (grade = 2), this returns d^2p(s,t)/d^2s; etc.
    
    Specified by:
    
    getSDerivative in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the derivative for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    grade - The grade to calculate the derivative for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    The specified s-derivative of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getSDerivative
```
public Vector<javax.measure.quantity.Length> getSDerivative(double s,
                                                            double t,
                                                            int grade)
```
    Calculate a derivative with respect to parametric s-distance of the given grade on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}s.
    Example:
    1st derivative (grade = 1), this returns dp(s,t)/ds;
    2nd derivative (grade = 2), this returns d^2p(s,t)/d^2s; etc.
    
    Specified by:
    
    getSDerivative in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The grade to calculate the derivative for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    The specified s-derivative of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTDerivative
```
public Vector<javax.measure.quantity.Length> getTDerivative(GeomPoint st,
                                                            int grade)
```
    Calculate a derivative with respect to parametric t-distance of the given grade on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}t.
    Example:
    1st derivative (grade = 1), this returns dp(s,t)/dt;
    2nd derivative (grade = 2), this returns d^2p(s,t)/d^2t; etc.
    
    Specified by:
    
    getTDerivative in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the derivative for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    grade - The grade to calculate the derivative for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    The specified t-derivative of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTDerivative
```
public Vector<javax.measure.quantity.Length> getTDerivative(double s,
                                                            double t,
                                                            int grade)
```
    Calculate a derivative with respect to parametric t-distance of the given grade on the surface for the given parametric position on the surface, d^{grade}p(s,t)/d^{grade}t.
    Example:
    1st derivative (grade = 1), this returns dp(s,t)/dt;
    2nd derivative (grade = 2), this returns d^2p(s,t)/d^2t; etc.
    
    Specified by:
    
    getTDerivative in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate derivative for (0.0 to 1.0 inclusive).
    
    grade - The grade to calculate the derivative for (1=1st derivative, 2=2nd derivative, etc)
    
    Returns:
    
    The specified t-derivative of the surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the grade is < 0 or the parameter values are invalid.
  - getTwistVector
```
public Vector<javax.measure.quantity.Length> getTwistVector(GeomPoint st)
```
    Calculate the twist vector (d^2P/(ds*dt) = d(dP/ds)/dt) for this surface at the specified position on this surface.
    
    Specified by:
    
    getTwistVector in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the twist vector for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The twist vector of this surface at the specified parametric position.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the parameter values are invalid.
  - getNormal
```
public Vector<javax.measure.quantity.Dimensionless> getNormal(double s,
                                                              double t)
```
    Return the at least 3D normal vector for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getNormal in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate normal for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate normal for (0.0 to 1.0 inclusive).
    
    Returns:
    
    The at least 3D normal vector of the surface at the specified parametric position.
  - getNormal
```
public Vector<javax.measure.quantity.Dimensionless> getNormal(GeomPoint st)
```
    Return the normal vector for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getNormal in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the normal for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The normal vector of the surface at the specified parametric position.
  - getTangentPlane
```
public Plane getTangentPlane(double s,
                             double t)
```
    Return the tangent plane to this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getTangentPlane in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate tangent plane for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate tangent plane for (0.0 to 1.0 inclusive).
    
    Returns:
    
    The tangent plane of the surface at the specified parametric position.
  - getTangentPlane
```
public Plane getTangentPlane(GeomPoint st)
```
    Return the tangent plane to this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getTangentPlane in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the tangent plane for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The tangent plane of the surface at the specified parametric position.
  - getGaussianCurvature
```
public Parameter getGaussianCurvature(double s,
                                      double t)
```
    Returns the Gaussian Curvature for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getGaussianCurvature in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate curvature for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate curvature for (0.0 to 1.0 inclusive).
    
    Returns:
    
    The Gaussian curvature of the surface at the specified parametric position in units of 1/Length^2.
  - getGaussianCurvature
```
public Parameter getGaussianCurvature(GeomPoint st)
```
    Returns the Gaussian Curvature for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getGaussianCurvature in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the curvature for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The Gaussian curvature of the surface at the specified parametric position in units of 1/Length^2.
  - getMeanCurvature
```
public Parameter getMeanCurvature(GeomPoint st)
```
    Returns the Mean Curvature for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getMeanCurvature in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st - The parametric position to calculate the curvature for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    Returns:
    
    The Mean curvature of the surface at the specified parametric position in units of 1/Length.
  - getMeanCurvature
```
public Parameter getMeanCurvature(double s,
                                  double t)
```
    Returns the Mean Curvature for this surface at the given parametric position (s,t) on this surface.
    
    Specified by:
    
    getMeanCurvature in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s - 1st parametric dimension distance to calculate curvature for (0.0 to 1.0 inclusive).
    
    t - 2nd parametric dimension distance to calculate curvature for (0.0 to 1.0 inclusive).
    
    Returns:
    
    The Mean curvature of the surface at the specified parametric position in units of 1/Length.
  - getArea
```
public Parameter<javax.measure.quantity.Area> getArea(double eps)
```
    Return the surface area of this entire surface.
    
    Specified by:
    
    getArea in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    eps - The desired fractional accuracy on the surface area.
    
    Returns:
    
    the surface area of this surface.
  - getArea
```
public Parameter<javax.measure.quantity.Area> getArea(GeomPoint st1,
                                                      GeomPoint st2,
                                                      double eps)
```
    Return the surface area of a portion of this surface.
    
    Specified by:
    
    getArea in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st1 - The starting parametric position to calculate the area for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    st2 - The ending parametric position to calculate the area for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    eps - The desired fractional accuracy on the surface area.
    
    Returns:
    
    the surface area of a portion of this surface.
  - getArea
```
public Parameter<javax.measure.quantity.Area> getArea(double s1,
                                                      double t1,
                                                      double s2,
                                                      double t2,
                                                      double eps)
```
    Return the surface area of a portion of this surface.
    
    Specified by:
    
    getArea in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s1 - The starting 1st parametric dimension distance to calculate area for (0.0 to 1.0 inclusive).
    
    t1 - The starting 2nd parametric dimension distance to calculate area for (0.0 to 1.0 inclusive).
    
    s2 - The ending 1st parametric dimension distance to calculate area for (0.0 to 1.0 inclusive).
    
    t2 - The ending 2nd parametric dimension distance to calculate area for (0.0 to 1.0 inclusive).
    
    eps - The desired fractional accuracy on the surface area.
    
    Returns:
    
    the surface area of a portion of this surface.
  - getVolume
```
public Parameter<javax.measure.quantity.Volume> getVolume(double eps)
```
    Return the enclosed volume of this entire surface.
    
    Specified by:
    
    getVolume in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    eps - The desired fractional accuracy on the enclosed volume.
    
    Returns:
    
    the enclosed volume of this surface.
  - getVolume
```
public Parameter<javax.measure.quantity.Volume> getVolume(GeomPoint st1,
                                                          GeomPoint st2,
                                                          double eps)
```
    Return the enclosed volume of a portion of this surface.
    
    Specified by:
    
    getVolume in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    st1 - The starting parametric position to calculate the volume for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    st2 - The ending parametric position to calculate the volume for. Must be a 2-dimensional point with each value in the range 0 to 1.0. Units are ignored.
    
    eps - The desired fractional accuracy on the enclosed volume.
    
    Returns:
    
    the enclosed volume of a portion of this surface.
  - getVolume
```
public Parameter<javax.measure.quantity.Volume> getVolume(double s1,
                                                          double t1,
                                                          double s2,
                                                          double t2,
                                                          double eps)
```
    Return the enclosed volume of a portion of this surface.
    
    Specified by:
    
    getVolume in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    s1 - The starting 1st parametric dimension distance to calculate volume for (0.0 to 1.0 inclusive).
    
    t1 - The starting 2nd parametric dimension distance to calculate volume for (0.0 to 1.0 inclusive).
    
    s2 - The ending 1st parametric dimension distance to calculate volume for (0.0 to 1.0 inclusive).
    
    t2 - The ending 2nd parametric dimension distance to calculate volume for (0.0 to 1.0 inclusive).
    
    eps - The desired fractional accuracy on the enclosed volume.
    
    Returns:
    
    the enclosed volume of a portion of this surface.
  - extractGrid
```
public PointArray<SubrangePoint> extractGrid(GridRule gridRule,
                                             java.util.List<java.lang.Double> bottomSpacing,
                                             java.util.List<java.lang.Double> topSpacing,
                                             java.util.List<java.lang.Double> leftSpacing,
                                             java.util.List<java.lang.Double> rightSpacing)
```
    Return an array of SubrangePoint objects that are gridded onto the surface using the specified spacings and gridding rule. gridRule specifies whether the subdivision spacing is applied with respect to arc-length in real space or parameter space. If the spacing is arc-length, then the values are interpreted as fractions of the arc length of the edge curves from 0 to 1.
    
    Specified by:
    
    extractGrid in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    gridRule - Specifies whether the subdivision spacing is applied with respect to arc-length in real space or parameter space. May not be null.
    
    bottomSpacing - A list of values used to define the subdivision spacing along the T=0 parametric boundary of the surface. May not be null.
    
    topSpacing - An optional list of values used to define the subdivision spacing along the T=1 parametric boundary of the surface. If null is passed, the bottomSpacing is used for the top. If topSpacing is provided, then it must have the same number of values as the bottomSpacing.
    
    leftSpacing - A list of values used to define the subdivision spacing along the S=0 parametric boundary of the surface. May not be null.
    
    rightSpacing - An optional list of values used to define the subdivision spacing along the S=1 parametric boundary of the surface. If null is passed, the leftSpacing is used for the right. If rightSpacing is provided, then it must have the same number of values as the leftSpacing.
    
    Returns:
    
    An array of SubrangePoint objects gridded onto the surface at the specified parametric positions.
  - gridToTolerance
```
public PointArray<SubrangePoint> gridToTolerance(Parameter<javax.measure.quantity.Length> tol)
```
    Return an array of points that are gridded onto the surface with the number of points and spacing chosen to result in straight line segments between the points that have mid-points that are all within the specified tolerance of this surface.
    
    Specified by:
    
    gridToTolerance in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    tol - The maximum distance that a straight line between gridded points may deviate from this surface. May not be null or zero.
    
    Returns:
    
    An array of subrange points gridded onto the surface.
  - getClosest
```
public SubrangePoint getClosest(GeomPoint point,
                                double tol)
```
    Returns the closest point on this surface to the specified point.
    
    Specified by:
    
    getClosest in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    point - The point to find the closest point on this surface to. May not be null.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The SubrangePoint on this surface that is closest to the specified point.
  - getClosest
```
public SubrangePoint getClosest(GeomPoint point,
                                double nearS,
                                double nearT,
                                double tol)
```
    Returns the closest point on this surface to the specified point near the specified parametric position.
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    point - The point to find the closest point on this surface to. May not be null.
    
    nearS - The parametric s-position where the search for the closest point should begin.
    
    nearT - The parametric t-position where the search for the closest point should begin.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The SubrangePoint on this surface that is closest to the specified point near the specified parametric position.
  - getClosest
```
public PointArray<SubrangePoint> getClosest(java.util.List<? extends java.util.List<GeomPoint>> points,
                                            double tol)
```
    Returns the array of closest points on this surface to the specified array (list of lists) of points.
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    points - A list of lists of points to find the closest point on this surface to. May not be null.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The PointArray of SubrangePoint on this surface that is closest to the specified list of lists of points.
  - getFarthest
```
public SubrangePoint getFarthest(GeomPoint point,
                                 double tol)
```
    Returns the farthest point on this surface from the specified point.
    
    Specified by:
    
    getFarthest in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    getFarthest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    point - The point to find the farthest point on this surface from. May not be null.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The SubrangePoint on this surface that is farthest from the specified point.
  - getFarthest
```
public SubrangePoint getFarthest(GeomPoint point,
                                 double nearS,
                                 double nearT,
                                 double tol)
```
    Returns the farthest point on this surface from the specified point near the specified parametric position on the surface.
    
    Specified by:
    
    getFarthest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    point - The point to find the farthest point on this surface from. May not be null.
    
    nearS - The parametric s-position where the search for the closest point should begin.
    
    nearT - The parametric t-position where the search for the closest point should begin.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The SubrangePoint on this surface that is farthest from the specified point.
  - getFarthest
```
public PointArray<SubrangePoint> getFarthest(java.util.List<? extends java.util.List<GeomPoint>> points,
                                             double tol)
```
    Returns the array of farthest points on this surface from the specified array (list of lists) of points.
    
    Specified by:
    
    getFarthest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    points - A list of lists of points to find the farthest point on this surface from. May not be null.
    
    tol - Fractional tolerance to refine the distance to.
    
    Returns:
    
    The PointArray of SubrangePoint on this surface that is farthest from the specified list of lists of points.
  - getClosest
```
public PointString<SubrangePoint> getClosest(Curve curve,
                                             double tol)
```
    Returns the closest points (giving the minimum distance) between this surface and the specified curve. If the specified curve intersects this surface, then the 1st intersection found is returned (not all the intersections are found and there is no guarantee about which intersection will be returned). If the specified curve is parallel to this surface (all points are equidistant away), then any point between this surface and the specified curve could be returned as the "closest".
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    curve - The curve to find the closest points between this surface and that curve on. May not be null.
    
    tol - Fractional tolerance (in parameter space) to refine the point position to.
    
    Returns:
    
    A list containing two SubrangePoint objects that represent the closest point on this surface (index 0) and the closest point on the specified curve (index 1).
  - getClosest
```
public PointString<SubrangePoint> getClosest(Surface surface,
                                             double tol)
```
    Returns the closest points (giving the minimum distance) between this surface and the specified surface. If the specified surface intersects this surface, then the 1st intersection found is returned (not all the intersections are found and there is no guarantee about which intersection will be returned). If the specified surface is parallel to this surface (all points are equidistant away), then any point between this surface and the specified surface could be returned as the "closest".
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    surface - The surface to find the closest points between this surface and that surface on. May not be null.
    
    tol - Fractional tolerance (in parameter space) to refine the point position to.
    
    Returns:
    
    A list containing two SubrangePoint objects that represent the closest point on this surface (index 0) and the closest point on the specified surface (index 1).
  - getClosest
```
public SubrangePoint getClosest(GeomPlane plane,
                                double tol)
```
    Returns the closest point (giving the minimum distance) between this surface and the specified plane. If the specified plane intersects this surface, then the 1st intersection found is returned (not all the intersections are found and there is no guarantee about which intersection will be returned). If the specified plane is parallel to this surface (all points are equidistant away), then any point between this surface and the specified plane could be returned as the "closest".
    
    Specified by:
    
    getClosest in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    plane - The plane to find the closest points between this surface and that plane on. May not be null.
    
    tol - Fractional tolerance (in parameter space) to refine the point position to.
    
    Returns:
    
    A SubrangePoint that represent the closest point on this surface to the specified plane.
  - getLimitPoint
```
public SubrangePoint getLimitPoint(int dim,
                                   boolean max,
                                   double tol)
```
    Returns the most extreme point, either minimum or maximum, in the specified coordinate direction on this surface. This is more accurate than getBoundsMax() & getBoundsMin(), but also typically takes longer to compute.
    
    Specified by:
    
    getLimitPoint in interface GeomElement<T extends AbstractSurface>
    
    Parameters:
    
    dim - An index indicating the dimension to find the min/max point for (0=X, 1=Y, 2=Z, etc).
    
    max - Set to true to return the maximum value, false to return the minimum.
    
    tol - Fractional tolerance (in parameter space) to refine the min/max point position to.
    
    Returns:
    
    The point found on this surface that is the min or max in the specified coordinate direction.
    
    See Also:
    
    GeomElement.getBoundsMin(), GeomElement.getBoundsMax()
  - intersect
```
public PointString<SubrangePoint> intersect(GeomPoint L0,
                                            GeomVector Ldir,
                                            Parameter<javax.measure.quantity.Length> tol)
```
    Return the intersections between an infinite line and this surface.
    
    Specified by:
    
    intersect in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    L0 - A point on the line (origin of the line). May not be null.
    
    Ldir - The direction vector for the line (does not have to be a unit vector). May not be null.
    
    tol - Tolerance (in physical space) to refine the point positions to. May not be null.
    
    Returns:
    
    A PointString containing zero or more subrange points made by the intersection of this surface with the specified infinite line. If no intersection is found, an empty PointString is returned.
  - intersect
```
public GeomList<PointString<SubrangePoint>> intersect(LineSegment line,
                                                      Parameter<javax.measure.quantity.Length> tol)
```
    Return the intersections between a line segment and this surface.
    
    Specified by:
    
    intersect in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    line - A line segment to intersect with this surface. May not be null.
    
    tol - Tolerance (in physical space) to refine the point positions to. May not be null.
    
    Returns:
    
    A list containing two PointString instances each containing zero or more subrange points, on this surface and the input line segment respectively, made by the intersection of this surface with the specified line segment. If no intersections are found a list of two empty PointStrings are returned.
  - intersect
```
public GeomList<PointString<SubrangePoint>> intersect(Curve curve,
                                                      Parameter<javax.measure.quantity.Length> tol)
```
    Return the intersections between a curve and this surface.
    
    Specified by:
    
    intersect in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    curve - The curve to intersect with this surface. May not be null.
    
    tol - Tolerance (in physical space) to refine the point positions to. May not be null.
    
    Returns:
    
    A list containing two PointString instances each containing zero or more subrange points, on this surface and the input curve respectively, made by the intersection of this surface with the specified curve. If no intersections are found a list of two empty PointStrings are returned.
  - intersect
```
public GeomList<SubrangeCurve> intersect(GeomPlane plane,
                                         Parameter<javax.measure.quantity.Length> tol)
```
    Return the intersections between an infinite plane and this surface.
    
    Specified by:
    
    intersect in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    plane - The infinite plane to intersect with this surface. May not be null.
    
    tol - Tolerance (in physical space) to refine the point positions to. May not be null.
    
    Returns:
    
    A PointString containing zero or more subrange points made by the intersection of this surface with the specified infinite plane. If no intersection is found, an empty PointString is returned.
  - intersect
```
public GeomList<GeomList<SubrangeCurve>> intersect(Surface surface,
                                                   Parameter<javax.measure.quantity.Length> tol)
```
    Return the intersections between another surface and this surface.
    
    Specified by:
    
    intersect in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    surface - A surface to intersect with this surface. May not be null.
    
    tol - Tolerance (in physical space) to refine the point positions to. May not be null.
    
    Returns:
    
    A list containing two lists of SubrangeCurve objects. Each list contains zero or more subrange curves, on this surface and the input surface respectively, made by the intersection of this surface with the specified surface. If no intersections are found a list of two empty lists is returned.
  - isDegenerate
```
public boolean isDegenerate(Parameter<javax.measure.quantity.Length> tol)
```
    Return true if this surface is degenerate (i.e.: has area less than the specified tolerance squared).
    
    Specified by:
    
    isDegenerate in interface ParametricGeometry<T extends AbstractSurface>
    
    Specified by:
    
    isDegenerate in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    tol - The tolerance for determining if this surface is degenerate. May not be null.
    
    Returns:
    
    true if this surface is degenerate.
  - isPlanar
```
public boolean isPlanar(Parameter<javax.measure.quantity.Length> tol)
```
    Return true if this surface is planar or false if it is not.
    
    Specified by:
    
    isPlanar in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    tol - The geometric tolerance to use in determining if the surface is planar. May not be null.
    
    Returns:
    
    true if this surface is planar.
  - isPlanar
```
public boolean isPlanar(double epsFT,
                        double epsELT)
```
    Return true if this surface is planar or false if it is not.
    
    Specified by:
    
    isPlanar in interface Surface<T extends AbstractSurface>
    
    Parameters:
    
    epsFT - Flatness tolerance (cosine of the angle allowable between normal vectors).
    
    epsELT - Edge linearity tolerance (cosine of the angle allowable between edge vectors).
    
    Returns:
    
    true if this surface is planar.

Class AbstractSurface<T extends AbstractSurface>

Field Summary

Fields inherited from class geomss.geom.AbstractGeomElement

Constructor Summary

Method Summary

Methods inherited from class geomss.geom.AbstractGeomElement

Methods inherited from class java.lang.Object

Methods inherited from interface java.lang.Comparable

Methods inherited from interface geomss.geom.GeomElement

Methods inherited from interface geomss.geom.Surface

Methods inherited from interface geomss.geom.Transformable

Field Detail

GTOL

Constructor Detail

AbstractSurface

Method Detail

getParDimension

transpose

splitAtS

splitAtT

getPoint

getPoint

getRealPoint

getCurve

getSCurve

getTCurve

getDerivatives

getSDerivatives

getSDerivatives

getSDerivatives

getTDerivatives

getTDerivatives

getTDerivatives

getSDerivative

getSDerivative

getTDerivative

getTDerivative

getTwistVector

getNormal

getNormal

getTangentPlane

getTangentPlane

getGaussianCurvature

getGaussianCurvature

getMeanCurvature

getMeanCurvature

getArea

getArea

getArea

getVolume

getVolume

getVolume

extractGrid

gridToTolerance

getClosest

getClosest

getClosest

getFarthest

getFarthest

getFarthest

getClosest

getClosest

getClosest

getLimitPoint

intersect

intersect

intersect

intersect

intersect

isDegenerate

isPlanar

isPlanar