adaptive-bezier-curve/function.js

adaptive and scalable 2D bezier curves

function clone(point) { //TODO: use gl-vec2 for this
    return [point[0], point[1]]
}

function vec2(x, y) {
    return [x, y]
}

module.exports = function createBezierBuilder(opt) {
    opt = opt||{}

    var RECURSION_LIMIT = typeof opt.recursion === 'number' ? opt.recursion : 8
    var FLT_EPSILON = typeof opt.epsilon === 'number' ? opt.epsilon : 1.19209290e-7
    var PATH_DISTANCE_EPSILON = typeof opt.pathEpsilon === 'number' ? opt.pathEpsilon : 1.0

    var curve_angle_tolerance_epsilon = typeof opt.angleEpsilon === 'number' ? opt.angleEpsilon : 0.01
    var m_angle_tolerance = opt.angleTolerance || 0
    var m_cusp_limit = opt.cuspLimit || 0

    return function bezierCurve(start, c1, c2, end, scale, points) {
        if (!points)
            points = []

        scale = typeof scale === 'number' ? scale : 1.0
        var distanceTolerance = PATH_DISTANCE_EPSILON / scale
        distanceTolerance *= distanceTolerance
        begin(start, c1, c2, end, points, distanceTolerance)
        return points
    }


    ////// Based on:
    ////// https://github.com/pelson/antigrain/blob/master/agg-2.4/src/agg_curves.cpp

    function begin(start, c1, c2, end, points, distanceTolerance) {
        points.push(clone(start))
        var x1 = start[0],
            y1 = start[1],
            x2 = c1[0],
            y2 = c1[1],
            x3 = c2[0],
            y3 = c2[1],
            x4 = end[0],
            y4 = end[1]
        recursive(x1, y1, x2, y2, x3, y3, x4, y4, points, distanceTolerance, 0)
        points.push(clone(end))
    }

    function recursive(x1, y1, x2, y2, x3, y3, x4, y4, points, distanceTolerance, level) {
        if(level > RECURSION_LIMIT) 
            return

        var pi = Math.PI

        // Calculate all the mid-points of the line segments
        //----------------------
        var x12   = (x1 + x2) / 2
        var y12   = (y1 + y2) / 2
        var x23   = (x2 + x3) / 2
        var y23   = (y2 + y3) / 2
        var x34   = (x3 + x4) / 2
        var y34   = (y3 + y4) / 2
        var x123  = (x12 + x23) / 2
        var y123  = (y12 + y23) / 2
        var x234  = (x23 + x34) / 2
        var y234  = (y23 + y34) / 2
        var x1234 = (x123 + x234) / 2
        var y1234 = (y123 + y234) / 2

        if(level > 0) { // Enforce subdivision first time
            // Try to approximate the full cubic curve by a single straight line
            //------------------
            var dx = x4-x1
            var dy = y4-y1

            var d2 = Math.abs((x2 - x4) * dy - (y2 - y4) * dx)
            var d3 = Math.abs((x3 - x4) * dy - (y3 - y4) * dx)

            var da1, da2

            if(d2 > FLT_EPSILON && d3 > FLT_EPSILON) {
                // Regular care
                //-----------------
                if((d2 + d3)*(d2 + d3) <= distanceTolerance * (dx*dx + dy*dy)) {
                    // If the curvature doesn't exceed the distanceTolerance value
                    // we tend to finish subdivisions.
                    //----------------------
                    if(m_angle_tolerance < curve_angle_tolerance_epsilon) {
                        points.push(vec2(x1234, y1234))
                        return
                    }

                    // Angle & Cusp Condition
                    //----------------------
                    var a23 = Math.atan2(y3 - y2, x3 - x2)
                    da1 = Math.abs(a23 - Math.atan2(y2 - y1, x2 - x1))
                    da2 = Math.abs(Math.atan2(y4 - y3, x4 - x3) - a23)
                    if(da1 >= pi) da1 = 2*pi - da1
                    if(da2 >= pi) da2 = 2*pi - da2

                    if(da1 + da2 < m_angle_tolerance) {
                        // Finally we can stop the recursion
                        //----------------------
                        points.push(vec2(x1234, y1234))
                        return
                    }

                    if(m_cusp_limit !== 0.0) {
                        if(da1 > m_cusp_limit) {
                            points.push(vec2(x2, y2))
                            return
                        }

                        if(da2 > m_cusp_limit) {
                            points.push(vec2(x3, y3))
                            return
                        }
                    }
                }
            }
            else {
                if(d2 > FLT_EPSILON) {
                    // p1,p3,p4 are collinear, p2 is considerable
                    //----------------------
                    if(d2 * d2 <= distanceTolerance * (dx*dx + dy*dy)) {
                        if(m_angle_tolerance < curve_angle_tolerance_epsilon) {
                            points.push(vec2(x1234, y1234))
                            return
                        }

                        // Angle Condition
                        //----------------------
                        da1 = Math.abs(Math.atan2(y3 - y2, x3 - x2) - Math.atan2(y2 - y1, x2 - x1))
                        if(da1 >= pi) da1 = 2*pi - da1

                        if(da1 < m_angle_tolerance) {
                            points.push(vec2(x2, y2))
                            points.push(vec2(x3, y3))
                            return
                        }

                        if(m_cusp_limit !== 0.0) {
                            if(da1 > m_cusp_limit) {
                                points.push(vec2(x2, y2))
                                return
                            }
                        }
                    }
                }
                else if(d3 > FLT_EPSILON) {
                    // p1,p2,p4 are collinear, p3 is considerable
                    //----------------------
                    if(d3 * d3 <= distanceTolerance * (dx*dx + dy*dy)) {
                        if(m_angle_tolerance < curve_angle_tolerance_epsilon) {
                            points.push(vec2(x1234, y1234))
                            return
                        }

                        // Angle Condition
                        //----------------------
                        da1 = Math.abs(Math.atan2(y4 - y3, x4 - x3) - Math.atan2(y3 - y2, x3 - x2))
                        if(da1 >= pi) da1 = 2*pi - da1

                        if(da1 < m_angle_tolerance) {
                            points.push(vec2(x2, y2))
                            points.push(vec2(x3, y3))
                            return
                        }

                        if(m_cusp_limit !== 0.0) {
                            if(da1 > m_cusp_limit)
                            {
                                points.push(vec2(x3, y3))
                                return
                            }
                        }
                    }
                }
                else {
                    // Collinear case
                    //-----------------
                    dx = x1234 - (x1 + x4) / 2
                    dy = y1234 - (y1 + y4) / 2
                    if(dx*dx + dy*dy <= distanceTolerance) {
                        points.push(vec2(x1234, y1234))
                        return
                    }
                }
            }
        }

        // Continue subdivision
        //----------------------
        recursive(x1, y1, x12, y12, x123, y123, x1234, y1234, points, distanceTolerance, level + 1) 
        recursive(x1234, y1234, x234, y234, x34, y34, x4, y4, points, distanceTolerance, level + 1) 
    }
}