Test if two lines intersect - JavaScript function

Question

I've tried searching for a javascript function that will detect if two lines intersect each other.

The function will take the x,y values of both the start end points for each line (we'll call them line A and line B).

Is to return true if they intersect, otherwise false.

Example of the function. I'm happy if the answer uses a vector object instead.

Function isIntersect (lineAp1x, lineAp1y, lineAp2x, lineAp2y, lineBp1x, lineBp1y, lineBp2x, lineBp2y) 
{

    // JavaScript line intersecting test here. 

}

Some background info: this code is for a game I'm trying to make in html5 canvas, and is part of my collision detection.

Answer 1

For all folks who would like to have a solutions ready for coldfusion, here is what I adapted from http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7-b147/java/awt/geom/Line2D.java#Line2D.linesIntersect%28double%2Cdouble%2Cdouble%2Cdouble%2Cdouble%2Cdouble%2Cdouble%2Cdouble%29

the imporants functions are ccw and linesIntersect from java.awt.geom.Line2D and I wrote them into coldfusion, so here we go:

<cffunction name="relativeCCW" description="schnittpunkt der vier punkte (2 geraden) berechnen">
<!---
Returns an indicator of where the specified point (px,py) lies with respect to this line segment. See the method comments of relativeCCW(double,double,double,double,double,double) to interpret the return value.
Parameters:
px the X coordinate of the specified point to be compared with this Line2D
py the Y coordinate of the specified point to be compared with this Line2D
Returns:
an integer that indicates the position of the specified coordinates with respect to this Line2D
--->
<cfargument name="x1" type="numeric" required="yes" >
<cfargument name="y1" type="numeric" required="yes">
<cfargument name="x2" type="numeric" required="yes" >
<cfargument name="y2" type="numeric" required="yes">
<cfargument name="px" type="numeric" required="yes" >
<cfargument name="py" type="numeric" required="yes">
    <cfscript>
    x2 = x2 - x1;
    y2 = y2 - y1;
    px = px - x1;
    py = py - y1;
    ccw = (px * y2) - (py * x2);
    if (ccw EQ 0) {
        // The point is colinear, classify based on which side of
        // the segment the point falls on.  We can calculate a
        // relative value using the projection of px,py onto the
        // segment - a negative value indicates the point projects
        // outside of the segment in the direction of the particular
        // endpoint used as the origin for the projection.
        ccw = (px * x2) + (py * y2);
        if (ccw GT 0) {
            // Reverse the projection to be relative to the original x2,y2
            // x2 and y2 are simply negated.
            // px and py need to have (x2 - x1) or (y2 - y1) subtracted
            //    from them (based on the original values)
            // Since we really want to get a positive answer when the
             //    point is "beyond (x2,y2)", then we want to calculate
            //    the inverse anyway - thus we leave x2 & y2 negated.       
            px = px - x2;
            py = py - y2;
            ccw = (px * x2) + (py * y2);
            if (ccw LT 0) {
                ccw = 0;
                }
        }
    }
    if (ccw LT 0) {
        ret = -1;
    }
    else if (ccw GT 0) {
        ret = 1;
    }
    else {
        ret = 0;
    }   
    </cfscript> 
    <cfreturn ret>
</cffunction>


<cffunction name="linesIntersect" description="schnittpunkt der vier punkte (2 geraden) berechnen">
<cfargument name="x1" type="numeric" required="yes" >
<cfargument name="y1" type="numeric" required="yes">
<cfargument name="x2" type="numeric" required="yes" >
<cfargument name="y2" type="numeric" required="yes">
<cfargument name="x3" type="numeric" required="yes" >
<cfargument name="y3" type="numeric" required="yes">
<cfargument name="x4" type="numeric" required="yes" >
<cfargument name="y4" type="numeric" required="yes">
    <cfscript>
    a1 = relativeCCW(x1, y1, x2, y2, x3, y3);
    a2 = relativeCCW(x1, y1, x2, y2, x4, y4);
    a3 = relativeCCW(x3, y3, x4, y4, x1, y1);
    a4 = relativeCCW(x3, y3, x4, y4, x2, y2);
    aa = ((relativeCCW(x1, y1, x2, y2, x3, y3) * relativeCCW(x1, y1, x2, y2, x4, y4) LTE 0)
            && (relativeCCW(x3, y3, x4, y4, x1, y1) * relativeCCW(x3, y3, x4, y4, x2, y2) LTE 0));
    </cfscript>
 <cfreturn aa>
</cffunction>

I hope this can help for adapting to other laguages?

Answer 2

First, find intersection coordinates - here it's described in detail: http://www.mathopenref.com/coordintersection.html

Then check if the x-coordinate for intersection falls within the x ranges for one of the lines (or do the same with y-coordinate, if you prefer), i.e. if xIntersection is between lineAp1x and lineAp2x, then they intersect.