Calculating the angle between two lines without having to calculate the slope? (Java)

user_402900 0
Viewed 73418

I have two Lines: L1 and L2. I want to calculate the angle between the two lines. L1 has points: {(x1, y1), (x2, y2)} and L2 has points: {(x3, y3), (x4, y4)}.

How can I calculate the angle formed between these two lines, without having to calculate the slopes? The problem I am currently having is that sometimes I have horizontal lines (lines along the x-axis) and the following formula fails (divide by zero exception): 

arctan((m1 - m2) / (1 - (m1 * m2)))

where m1 and m2 are the slopes of line 1 and line 2 respectively. Is there a formula/algorithm that can calculate the angles between the two lines without ever getting divide-by-zero exceptions? Any help would be highly appreciated.

This is my code snippet:

// Calculates the angle formed between two lines
public static double angleBetween2Lines(Line2D line1, Line2D line2)
{
    double slope1 = line1.getY1() - line1.getY2() / line1.getX1() - line1.getX2();
    double slope2 = line2.getY1() - line2.getY2() / line2.getX1() - line2.getX2();
    double angle = Math.atan((slope1 - slope2) / (1 - (slope1 * slope2)));
    return angle;
}

Thanks.

trigonometry coordinates math geometry java
8 Answers

Maybe my approach for Android coordinates system will be useful for someone (used Android PointF class to store points)

/**
 * Calculate angle between two lines with two given points
 *
 * @param A1 First point first line
 * @param A2 Second point first line
 * @param B1 First point second line
 * @param B2 Second point second line
 * @return Angle between two lines in degrees
 */

public static float angleBetween2Lines(PointF A1, PointF A2, PointF B1, PointF B2) {
    float angle1 = (float) Math.atan2(A2.y - A1.y, A1.x - A2.x);
    float angle2 = (float) Math.atan2(B2.y - B1.y, B1.x - B2.x);
    float calculatedAngle = (float) Math.toDegrees(angle1 - angle2);
    if (calculatedAngle < 0) calculatedAngle += 360;
    return calculatedAngle;
}

It return positive value in degrees for any quadrant: 0 <= x < 360

You can checkout my utility class here

user_12296740

Check this Python code:

import math
def angle(x1,y1,x2,y2,x3,y3):

  if (x1==x2==x3 or y1==y2==y3):
    return 180
  else:
    dx1 = x2-x1
    dy1 = y2-y1
    dx2 = x3-x2
    dy2 = y3-y2
    if x1==x2:
      a1=90
    else:
      m1=dy1/dx1
      a1=math.degrees(math.atan(m1))
    if x2==x3:
      a2=90
    else:
      m2=dy2/dx2
      a2=math.degrees(math.atan(m2))
    angle = abs(a2-a1)
    return angle

print angle(0,4,0,0,9,-6)
user_98635510 
dx1=x2-x1 ; dy1=y2-y1 ; dx2=x4-x3 ;dy2=y4-y3.

Angle(L1,L2)=pi()/2*((1+sign(dx1))* (1-sign(dy1^2))-(1+sign(dx2))*(1-sign(dy2^2)))
           +pi()/4*((2+sign(dx1))*sign(dy1)-(2+sign(dx2))*sign(dy2))
           +sign(dx1*dy1)*atan((abs(dx1)-abs(dy1))/(abs(dx1)+abs(dy1)))
           -sign(dx2*dy2)*atan((abs(dx2)-abs(dy2))/(abs(dx2)+abs(dy2)))
user_105728670
Related