Package com.badlogic.gdx.math

Class GeometryUtils

  • public final class GeometryUtils
extends java.lang.Object

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static boolean barycoordInsideTriangle​(Vector2 barycentric)
      Returns true if the barycentric coordinates are inside the triangle.
      static boolean colinear​(float x1, float y1, float x2, float y2, float x3, float y3)  
      static void ensureCCW​(float[] polygon)  
      static void ensureCCW​(float[] polygon, int offset, int count)  
      static void ensureClockwise​(float[] polygon)  
      static void ensureClockwise​(float[] polygon, int offset, int count)  
      static float fromBarycoord​(Vector2 barycentric, float a, float b, float c)
      Returns an interpolated value given the barycentric coordinates of a point in a triangle and the values at each vertex.
      static Vector2 fromBarycoord​(Vector2 barycentric, Vector2 a, Vector2 b, Vector2 c, Vector2 interpolatedOut)
      Returns interpolated values given the barycentric coordinates of a point in a triangle and the values at each vertex.
      static boolean isCCW​(float[] polygon, int offset, int count)  
      static boolean isClockwise​(float[] polygon, int offset, int count)  
      static float lowestPositiveRoot​(float a, float b, float c)
      Returns the lowest positive root of the quadric equation given by a * x * x + b * x + c = 0.
      static float polygonArea​(float[] polygon, int offset, int count)
      Computes the area for a convex polygon.
      static Vector2 polygonCentroid​(float[] polygon, int offset, int count, Vector2 centroid)
      Returns the centroid for the specified non-self-intersecting polygon.
      static Vector2 quadrilateralCentroid​(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4, Vector2 centroid)  
      static void reverseVertices​(float[] polygon, int offset, int count)  
      static Vector2 toBarycoord​(Vector2 p, Vector2 a, Vector2 b, Vector2 c, Vector2 barycentricOut)
      Computes the barycentric coordinates v,w for the specified point in the triangle.
      static float triangleArea​(float x1, float y1, float x2, float y2, float x3, float y3)  
      static Vector2 triangleCentroid​(float x1, float y1, float x2, float y2, float x3, float y3, Vector2 centroid)  
      static Vector2 triangleCircumcenter​(float x1, float y1, float x2, float y2, float x3, float y3, Vector2 circumcenter)
      Returns the circumcenter of the triangle.
      static float triangleCircumradius​(float x1, float y1, float x2, float y2, float x3, float y3)  
      static float triangleQuality​(float x1, float y1, float x2, float y2, float x3, float y3)
      Ratio of circumradius to shortest edge as a measure of triangle quality.

      • Methods inherited from class java.lang.Object

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

    • Method Detail

      • toBarycoord

        public static Vector2 toBarycoord​(Vector2 p,
                                  Vector2 a,
                                  Vector2 b,
                                  Vector2 c,
                                  Vector2 barycentricOut)
        Computes the barycentric coordinates v,w for the specified point in the triangle.

        If barycentric.x >= 0 && barycentric.y >= 0 && barycentric.x + barycentric.y <= 1 then the point is inside the triangle.

        If vertices a,b,c have values aa,bb,cc then to get an interpolated value at point p: 

         GeometryUtils.toBarycoord(p, a, b, c, barycentric);
 // THEN:
 float u = 1f - barycentric.x - barycentric.y;
 float x = u * aa.x + barycentric.x * bb.x + barycentric.y * cc.x;
 float y = u * aa.y + barycentric.x * bb.y + barycentric.y * cc.y;
 // OR:
 GeometryUtils.fromBarycoord(barycentric, aa, bb, cc, out);
        Returns:
        barycentricOut

      • barycoordInsideTriangle

        public static boolean barycoordInsideTriangle​(Vector2 barycentric)
        Returns true if the barycentric coordinates are inside the triangle.

      • fromBarycoord

        public static Vector2 fromBarycoord​(Vector2 barycentric,
                                    Vector2 a,
                                    Vector2 b,
                                    Vector2 c,
                                    Vector2 interpolatedOut)
        Returns interpolated values given the barycentric coordinates of a point in a triangle and the values at each vertex.
        Returns:
        interpolatedOut

      • fromBarycoord

        public static float fromBarycoord​(Vector2 barycentric,
                                  float a,
                                  float b,
                                  float c)
        Returns an interpolated value given the barycentric coordinates of a point in a triangle and the values at each vertex.
        Returns:
        interpolatedOut

      • lowestPositiveRoot

        public static float lowestPositiveRoot​(float a,
                                       float b,
                                       float c)
        Returns the lowest positive root of the quadric equation given by a * x * x + b * x + c = 0. If no solution is given, Float.NaN is returned.
        Parameters:
        a - the first coefficient of the quadric equation
        b - the second coefficient of the quadric equation
        c - the third coefficient of the quadric equation
        Returns:
        the lowest positive root or Float.Nan

      • colinear

        public static boolean colinear​(float x1,
                               float y1,
                               float x2,
                               float y2,
                               float x3,
                               float y3)

      • triangleCentroid

        public static Vector2 triangleCentroid​(float x1,
                                       float y1,
                                       float x2,
                                       float y2,
                                       float x3,
                                       float y3,
                                       Vector2 centroid)

      • triangleCircumcenter

        public static Vector2 triangleCircumcenter​(float x1,
                                           float y1,
                                           float x2,
                                           float y2,
                                           float x3,
                                           float y3,
                                           Vector2 circumcenter)
        Returns the circumcenter of the triangle. The input points must not be colinear.

      • triangleCircumradius

        public static float triangleCircumradius​(float x1,
                                         float y1,
                                         float x2,
                                         float y2,
                                         float x3,
                                         float y3)

      • triangleQuality

        public static float triangleQuality​(float x1,
                                    float y1,
                                    float x2,
                                    float y2,
                                    float x3,
                                    float y3)
        Ratio of circumradius to shortest edge as a measure of triangle quality.

        Gary L. Miller, Dafna Talmor, Shang-Hua Teng, and Noel Walkington. A Delaunay Based Numerical Method for Three Dimensions: Generation, Formulation, and Partition.

      • triangleArea

        public static float triangleArea​(float x1,
                                 float y1,
                                 float x2,
                                 float y2,
                                 float x3,
                                 float y3)

      • quadrilateralCentroid

        public static Vector2 quadrilateralCentroid​(float x1,
                                            float y1,
                                            float x2,
                                            float y2,
                                            float x3,
                                            float y3,
                                            float x4,
                                            float y4,
                                            Vector2 centroid)

      • polygonCentroid

        public static Vector2 polygonCentroid​(float[] polygon,
                                      int offset,
                                      int count,
                                      Vector2 centroid)
        Returns the centroid for the specified non-self-intersecting polygon.

      • polygonArea

        public static float polygonArea​(float[] polygon,
                                int offset,
                                int count)
        Computes the area for a convex polygon.

      • ensureCCW

        public static void ensureCCW​(float[] polygon)

      • ensureCCW

        public static void ensureCCW​(float[] polygon,
                             int offset,
                             int count)

      • ensureClockwise

        public static void ensureClockwise​(float[] polygon)

      • ensureClockwise

        public static void ensureClockwise​(float[] polygon,
                                   int offset,
                                   int count)

      • reverseVertices

        public static void reverseVertices​(float[] polygon,
                                   int offset,
                                   int count)

      • isClockwise

        public static boolean isClockwise​(float[] polygon,
                                  int offset,
                                  int count)

      • isCCW

        public static boolean isCCW​(float[] polygon,
                            int offset,
                            int count)