org.opensourcephysics.display
Class GraphicsLib

java.lang.Object
  org.opensourcephysics.display.GraphicsLib

public class GraphicsLib
extends java.lang.Object

Library of useful computer graphics routines such as geometry routines for computing the intersection of different shapes and rendering methods for computing bounds and performing optimized drawing.

Author:

jeffrey heer

Field Summary

static int	COINCIDENT Indicates intersection between shapes
static int	NO_INTERSECTION Indicates no intersection between shapes
static int	PARALLEL Indicates two lines are parallel

Constructor Summary

GraphicsLib()

Method Summary

static java.awt.geom.GeneralPath	cardinalSpline(float[] pts, float slack, boolean closed) Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points.
static java.awt.geom.GeneralPath	cardinalSpline(float[] pts, int start, int npoints, float slack, boolean closed) Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points.
static java.awt.geom.GeneralPath	cardinalSpline(java.awt.geom.GeneralPath p, float[] pts, float slack, boolean closed, float tx, float ty) Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points.
static java.awt.geom.GeneralPath	cardinalSpline(java.awt.geom.GeneralPath p, float[] pts, int start, int npoints, float slack, boolean closed, float tx, float ty) Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points.
static float[]	centroid(float[] pts, int len) Computes the mean, or centroid, of a set of points
static double[]	convexHull(double[] pts, int len) Computes the 2D convex hull of a set of points using Graham's scanning algorithm.
static double[]	convexHull(double[] pts, int len, float[] angles, int[] idx, int[] stack) Computes the 2D convex hull of a set of points using Graham's scanning algorithm.
static void	expand(java.awt.geom.Rectangle2D r, double amount) Expand a rectangle by the given amount.
static void	growPolygon(float[] pts, int len, float amt) Expand a polygon by adding the given distance along the line from the centroid of the polyong.
static int	intersectLineLine(double a1x, double a1y, double a2x, double a2y, double b1x, double b1y, double b2x, double b2y, java.awt.geom.Point2D intersect) Compute the intersection of two line segments.
static int	intersectLineLine(java.awt.geom.Line2D a, java.awt.geom.Line2D b, java.awt.geom.Point2D intersect) Compute the intersection of two line segments.
static int	intersectLineRectangle(java.awt.geom.Line2D l, java.awt.geom.Rectangle2D r, java.awt.geom.Point2D[] pts) Compute the intersection of a line and a rectangle.
static int	intersectLineRectangle(java.awt.geom.Point2D a1, java.awt.geom.Point2D a2, java.awt.geom.Rectangle2D r, java.awt.geom.Point2D[] pts) Compute the intersection of a line and a rectangle.
static java.awt.geom.GeneralPath	stackSpline(java.awt.geom.GeneralPath p, float[] pts, float epsilon, float slack, boolean closed, float tx, float ty) Computes a set of curves using the cardinal spline approach, but using straight lines for completely horizontal or vertical segments.
static java.awt.geom.GeneralPath	stackSpline(java.awt.geom.GeneralPath p, float[] pts, int start, int npoints, float epsilon, float slack, boolean closed, float tx, float ty) Computes a set of curves using the cardinal spline approach, but using straight lines for completely horizontal or vertical segments.

Methods inherited from class java.lang.Object

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

Field Detail

NO_INTERSECTION

public static final int NO_INTERSECTION

Indicates no intersection between shapes

See Also:

Constant Field Values

COINCIDENT

public static final int COINCIDENT

Indicates intersection between shapes

See Also:

Constant Field Values

PARALLEL

public static final int PARALLEL

Indicates two lines are parallel

See Also:

Constant Field Values

Constructor Detail

GraphicsLib

public GraphicsLib()

Method Detail

intersectLineLine

public static int intersectLineLine(java.awt.geom.Line2D a,
                                    java.awt.geom.Line2D b,
                                    java.awt.geom.Point2D intersect)

Compute the intersection of two line segments.

Parameters:

a - the first line segment

b - the second line segment

intersect - a Point in which to store the intersection point

Returns:

the intersection code. One of NO_INTERSECTION, COINCIDENT, or PARALLEL.

intersectLineLine

public static int intersectLineLine(double a1x,
                                    double a1y,
                                    double a2x,
                                    double a2y,
                                    double b1x,
                                    double b1y,
                                    double b2x,
                                    double b2y,
                                    java.awt.geom.Point2D intersect)

Compute the intersection of two line segments.

Parameters:

a1x - the x-coordinate of the first endpoint of the first line

a1y - the y-coordinate of the first endpoint of the first line

a2x - the x-coordinate of the second endpoint of the first line

a2y - the y-coordinate of the second endpoint of the first line

b1x - the x-coordinate of the first endpoint of the second line

b1y - the y-coordinate of the first endpoint of the second line

b2x - the x-coordinate of the second endpoint of the second line

b2y - the y-coordinate of the second endpoint of the second line

intersect - a Point in which to store the intersection point

Returns:

the intersection code. One of NO_INTERSECTION, COINCIDENT, or PARALLEL.

intersectLineRectangle

public static int intersectLineRectangle(java.awt.geom.Point2D a1,
                                         java.awt.geom.Point2D a2,
                                         java.awt.geom.Rectangle2D r,
                                         java.awt.geom.Point2D[] pts)

Compute the intersection of a line and a rectangle.

Parameters:

a1 - the first endpoint of the line

a2 - the second endpoint of the line

r - the rectangle

pts - a length 2 or greater array of points in which to store the results

Returns:

the intersection code. One of NO_INTERSECTION, COINCIDENT, or PARALLEL.

intersectLineRectangle

public static int intersectLineRectangle(java.awt.geom.Line2D l,
                                         java.awt.geom.Rectangle2D r,
                                         java.awt.geom.Point2D[] pts)

Compute the intersection of a line and a rectangle.

Parameters:

l - the line

r - the rectangle

pts - a length 2 or greater array of points in which to store the results

Returns:

the intersection code. One of NO_INTERSECTION, COINCIDENT, or PARALLEL.

convexHull

public static double[] convexHull(double[] pts,
                                  int len)

Computes the 2D convex hull of a set of points using Graham's scanning algorithm. The algorithm has been implemented as described in Cormen, Leiserson, and Rivest's Introduction to Algorithms. The running time of this algorithm is O(n log n), where n is the number of input points.

Parameters:

pts - the input points in [x0,y0,x1,y1,...] order

len - the length of the pts array to consider (2 * #points)

Returns:

the convex hull of the input points

convexHull

public static double[] convexHull(double[] pts,
                                  int len,
                                  float[] angles,
                                  int[] idx,
                                  int[] stack)

Computes the 2D convex hull of a set of points using Graham's scanning algorithm. The algorithm has been implemented as described in Cormen, Leiserson, and Rivest's Introduction to Algorithms. The running time of this algorithm is O(n log n), where n is the number of input points.

Parameters:

pts -

Returns:

the convex hull of the input points

centroid

public static float[] centroid(float[] pts,
                               int len)

Computes the mean, or centroid, of a set of points

Parameters:

pts - the points array, in x1, y1, x2, y2, ... arrangement.

len - the length of the array to consider

Returns:

the centroid as a length-2 float array

growPolygon

public static void growPolygon(float[] pts,
                               int len,
                               float amt)

Expand a polygon by adding the given distance along the line from the centroid of the polyong.

Parameters:

pts - the polygon to expand, a set of points in a float array

len - the length of the range of the array to consider

amt - the amount by which to expand the polygon, each point will be moved this distance along the line from the centroid of the polygon to the given point.

cardinalSpline

public static java.awt.geom.GeneralPath cardinalSpline(float[] pts,
                                                       float slack,
                                                       boolean closed)

Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points. Cardinal splines maintain C(1) continuity, ensuring the connected spline segments form a differentiable curve, ensuring at least a minimum level of smoothness.

Parameters:

pts - the points to interpolate with a cardinal spline

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the cardinal spline should be closed (i.e. return to the starting point), false for an open curve

Returns:

the cardinal spline as a Java2D GeneralPath instance.

cardinalSpline

public static java.awt.geom.GeneralPath cardinalSpline(float[] pts,
                                                       int start,
                                                       int npoints,
                                                       float slack,
                                                       boolean closed)

Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points. Cardinal splines maintain C(1) continuity, ensuring the connected spline segments form a differentiable curve, ensuring at least a minimum level of smoothness.

Parameters:

pts - the points to interpolate with a cardinal spline

start - the starting index from which to read points

npoints - the number of points to consider

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the cardinal spline should be closed (i.e. return to the starting point), false for an open curve

Returns:

the cardinal spline as a Java2D GeneralPath instance.

cardinalSpline

public static java.awt.geom.GeneralPath cardinalSpline(java.awt.geom.GeneralPath p,
                                                       float[] pts,
                                                       float slack,
                                                       boolean closed,
                                                       float tx,
                                                       float ty)

Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points. Cardinal splines maintain C(1) continuity, ensuring the connected spline segments form a differentiable curve, ensuring at least a minimum level of smoothness.

Parameters:

p - the GeneralPath instance to use to store the result

pts - the points to interpolate with a cardinal spline

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the cardinal spline should be closed (i.e. return to the starting point), false for an open curve

tx - a value by which to translate the curve along the x-dimension

ty - a value by which to translate the curve along the y-dimension

Returns:

the cardinal spline as a Java2D GeneralPath instance.

cardinalSpline

public static java.awt.geom.GeneralPath cardinalSpline(java.awt.geom.GeneralPath p,
                                                       float[] pts,
                                                       int start,
                                                       int npoints,
                                                       float slack,
                                                       boolean closed,
                                                       float tx,
                                                       float ty)

Compute a cardinal spline, a series of cubic Bezier splines smoothly connecting a set of points. Cardinal splines maintain C(1) continuity, ensuring the connected spline segments form a differentiable curve, ensuring at least a minimum level of smoothness.

Parameters:

p - the GeneralPath instance to use to store the result

pts - the points to interpolate with a cardinal spline

start - the starting index from which to read points

npoints - the number of points to consider

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the cardinal spline should be closed (i.e. return to the starting point), false for an open curve

tx - a value by which to translate the curve along the x-dimension

ty - a value by which to translate the curve along the y-dimension

Returns:

the cardinal spline as a Java2D GeneralPath instance.

stackSpline

public static java.awt.geom.GeneralPath stackSpline(java.awt.geom.GeneralPath p,
                                                    float[] pts,
                                                    float epsilon,
                                                    float slack,
                                                    boolean closed,
                                                    float tx,
                                                    float ty)

Computes a set of curves using the cardinal spline approach, but using straight lines for completely horizontal or vertical segments.

Parameters:

p - the GeneralPath instance to use to store the result

pts - the points to interpolate with the spline

epsilon - threshold value under which to treat the difference between two values to be zero. Used to determine which segments to treat as lines rather than curves.

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the spline should be closed (i.e. return to the starting point), false for an open curve

tx - a value by which to translate the curve along the x-dimension

ty - a value by which to translate the curve along the y-dimension

Returns:

the stack spline as a Java2D GeneralPath instance.

stackSpline

public static java.awt.geom.GeneralPath stackSpline(java.awt.geom.GeneralPath p,
                                                    float[] pts,
                                                    int start,
                                                    int npoints,
                                                    float epsilon,
                                                    float slack,
                                                    boolean closed,
                                                    float tx,
                                                    float ty)

Computes a set of curves using the cardinal spline approach, but using straight lines for completely horizontal or vertical segments.

Parameters:

p - the GeneralPath instance to use to store the result

pts - the points to interpolate with the spline

start - the starting index from which to read points

npoints - the number of points to consider

epsilon - threshold value under which to treat the difference between two values to be zero. Used to determine which segments to treat as lines rather than curves.

slack - a parameter controlling the "tightness" of the spline to the control points, 0.10 is a typically suitable value

closed - true if the spline should be closed (i.e. return to the starting point), false for an open curve

tx - a value by which to translate the curve along the x-dimension

ty - a value by which to translate the curve along the y-dimension

Returns:

the stack spline as a Java2D GeneralPath instance.

expand

public static void expand(java.awt.geom.Rectangle2D r,
                          double amount)

Expand a rectangle by the given amount.

Parameters:

r - the rectangle to expand

amount - the amount by which to expand the rectangle