Draw parallel lines along the path - PHP GD

Question

I need to draw something like a metro map (multiple routes on the same path) using the PHP image library. Here is an example:

  *********
  ******** *
  ******* * *
         * * *
          * * *
          * * *
          * * *
          * * *                      
          * * *                      
          * * *                      
           * * *                     
            * * *                    
             * * *                   
              * * *********************
               * **********************
                ***********************

It is easy enough to draw one line along this path. I do not know how to draw several lines that follow the path, but have an equal amount of space between them.

Answer 1

A , "" (B) "" (C):

  ********C
  D******A *
  Q*****B * *
         * * *
          * E *

B A = (, 5 ) , AE AD "" B ( AD AE "" C ). B 5px A A angle AE + ((angle AD - angle AE) / 2)

wiz, , , , javascript, , PHP (, , , ):

var dx = b.x - a.x;
var dy = b.y - a.y;
if(dx == 0 && dy == 0){
    answer = 0;
} else if(dx > 0 && dy >= 0 ){
    answer = Math.atan(dy/dx);
} else if(dx <= 0 && dy > 0){
    answer = Math.atan(dx/dy) + (Math.PI * 0.5);
} else if(dx <= 0 && dy <= 0){
    answer = Math.atan(dy/dx) + Math.PI;
} else if(dx >= 0 && dy <= 0){
    answer = Math.atan(dy/dx) + (Math.PI * 1.5);
}

, , D = (0,10), A = (10,10), E = (20,20):

• AE = 45 ° (PI/4 ), AD = 180 ° (PI )
• (45 + ((180-45)/2)) = > 112,5 ° (5/8 PI )
• 5px A = (10,10) 112,5 ° B:
  • Bx = Ax + (cos(angle) * 5) = +/- 8.1
  • By = Ay + (sin(angle) * 5) = +/- 14.6
• "sibling" Q, D, / , : DQ = DA + 90 ° (PI/2 ) ( Dy + 5, , , )
• , .

Answer 2

Wrikken, Objective-C cocos2d-iphone, . , -, . C .

A B, A C. cosf/sinf .

PS: for i = 0 i < numVertices.

CGPoint splinePoint = splinePoints[i];

CGPoint prevPoint = (i == 0) ? splinePoint : splinePoints[i - 1];
CGPoint railPoint = splinePoint;
CGPoint nextPoint = (i == (numVertices-1)) ? splinePoint : splinePoints[i + 1];

CGPoint toPrevPoint = ccpSub(railPoint, prevPoint);
CGPoint toNextPoint = ccpSub(railPoint, nextPoint);
float angleToPrevPoint = ccpAngleSigned(kAngleOriginVector, toPrevPoint);
float angleToNextPoint = ccpAngleSigned(kAngleOriginVector, toNextPoint);
float offsetAngle = 0.0f;

if (i > 0 && i < (numVertices - 1))
{
    offsetAngle = angleToNextPoint + ((angleToPrevPoint-angleToNextPoint) / 2);
}
else if (i == 0)
{
    offsetAngle = angleToNextPoint + M_PI_2;
}
else
{
    offsetAngle = angleToPrevPoint + M_PI_2;
}

CGPoint offsetLeftRail, offsetRightRail, offsetRail;
offsetRail.x = cosf(offsetAngle) * railOffsetFromCenter;
offsetRail.y = sinf(offsetAngle) * railOffsetFromCenter;
offsetLeftRail = ccpAdd(railPoint, offsetRail);
offsetRightRail = ccpAdd(railPoint, ccpMult(offsetRail, -1.0f));

if (isPointToTheLeftOfLine(prevPoint, railPoint, offsetLeftRail))
{
    leftRailSplinePoints[i] = offsetLeftRail;
    rightRailSplinePoints[i] = offsetRightRail;
}
else
{
    leftRailSplinePoints[i] = offsetRightRail;
    rightRailSplinePoints[i] = offsetLeftRail;
}

BOOL isPointToTheLeftOfLine(CGPoint start, CGPoint end, CGPoint test)
{
    return ((end.x - start.x) * (test.y - start.y) -
            (end.y - start.y) * (test.x - start.x)) > 0;
}

railtrack: