Module org.jhotdraw8.geom
Package org.jhotdraw8.geom.contour

Class BulgeConversionFunctions

java.lang.Object
org.jhotdraw8.geom.contour.BulgeConversionFunctions
public class BulgeConversionFunctions extends Object
Provides bulge conversion functions.

The curvature of a PlinePath arc segment is defined using a quantity known as bulge. This unit measures the deviation of the curve from the straight line (chord) joining the two vertices of the segment. It is defined as the ratio of the arc sagitta (versine) to half the length of the chord between the two vertices; this ratio is equal to the tangent of a quarter of the included arc angle between the two polyline vertices.

In this way, a negative bulge indicates that the arc follows a clockwise direction from the first vertex to the next, with a positive bulge describing an anticlockwise oriented arc. A bulge of 0 indicates a straight segment, and a bulge of 1 is a semicircle.

An AutoCAD Arc Entity is defined by a center, radius, start and end angle. The arc is always defined to be anticlockwise oriented, that is, following an anticlockwise direction from the start angle to the end angle.

References:

Bulge conversions
lee-mac.com

  • Method Details

    • computeCircle

      public static BulgeConversionFunctions.ArcRadiusAndCenter computeCircle(double x1, double y1, double x2, double y2, double b)
      This version uses the relationship between the arc sagitta and bulge factor, illustrated by the following diagram: 
                      .
         .      |    .
     .          |s        .
   .∡θ/4   d    |          .
 p1-------------+------------p2
    \                      /
       \                / r
          \    ∡θ    /
                c
      • chord = 2*d = |p1 - p2|
      • bulge = b = tan(θ/4)
      • angle = θ = 4*arctan(b)
      • sagitta = s = b * d
      • radius = r = (s^2+d^2)/(2*s) = d*(b^2+1)/(2*b)
      • half chord = d = r * sin(θ/2) = |p2 - p1|/2
      • c = polar(p1, atan2(p1,p2) + (pi - θ)/2, r)

    • computeBulge

      public static double computeBulge(double x1, double y1, double x2, double y2, double x3, double y3)
      This function will return the bulge value describing an arc which starts at the first supplied point pt1, passes through the second supplied point pt2, and terminates at the third supplied point pt3.

      The returned bulge value may be positive or negative, depending upon whether the arc passing through the three points traces a clockwise or counter-clockwise path.

      Parameters:
      x1 - point 1 x-coordinate
      y1 - point 1 y coordinate
      x2 - point 2 x-coordinate
      y2 - point 2 y coordinate
      x3 - point 3 x-coordinate
      y3 - point 3 y coordinate
      Returns:
      the bulge

    • computeBulge

      public static double computeBulge(double x1, double y1, double x2, double y2, double r)
      This function will return the bulge value describing an arc with the given radius which starts at the first supplied point pt1, and terminates at the third supplied point pt3.

      sin(θ/2)=d/r; θ=asin(d/r)*2; bulge=b=tan(θ/4)=tan(asin(d/r)*0.5)

      See computeCircle(double, double, double, double, double) for the formulas used.

      Parameters:
      x1 - point 1 x-coordinate
      y1 - point 1 y coordinate
      x2 - point 2 x-coordinate
      y2 - point 2 y coordinate
      r - the radius of the circle
      Returns:
      the bulge

    • arcRadiusAndCenter

      public static BulgeConversionFunctions.ArcRadiusAndCenter arcRadiusAndCenter(PlineVertex v1, PlineVertex v2)