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Improve epsilon logic #8

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74 changes: 41 additions & 33 deletions lib/epsilon.js
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Original file line number Diff line number Diff line change
Expand Up @@ -24,29 +24,28 @@ function Epsilon(eps){
var By = right[1];
var Cx = pt[0];
var Cy = pt[1];
return (Bx - Ax) * (Cy - Ay) - (By - Ay) * (Cx - Ax) >= -eps;
var ABx = Bx - Ax;
var ABy = By - Ay;
var AB = Math.sqrt(ABx * ABx + ABy * ABy);
// algebraic distance of 'pt' to ('left', 'right') line is:
// [ABx * (Cy - Ay) - ABy * (Cx - Ax)] / AB
return ABx * (Cy - Ay) - ABy * (Cx - Ax) >= -eps * AB;
},
pointBetween: function(p, left, right){
// p must be collinear with left->right
// returns false if p == left, p == right, or left == right
if (my.pointsSame(p, left) || my.pointsSame(p, right)) return false;
var d_py_ly = p[1] - left[1];
var d_rx_lx = right[0] - left[0];
var d_px_lx = p[0] - left[0];
var d_ry_ly = right[1] - left[1];

var dot = d_px_lx * d_rx_lx + d_py_ly * d_ry_ly;
// if `dot` is 0, then `p` == `left` or `left` == `right` (reject)
// if `dot` is less than 0, then `p` is to the left of `left` (reject)
if (dot < eps)
return false;

// dot < 0 is p is to the left of 'left'
if (dot < 0) return false;
var sqlen = d_rx_lx * d_rx_lx + d_ry_ly * d_ry_ly;
// if `dot` > `sqlen`, then `p` is to the right of `right` (reject)
// therefore, if `dot - sqlen` is greater than 0, then `p` is to the right of `right` (reject)
if (dot - sqlen > -eps)
return false;

return true;
// dot <= sqlen is p is to the left of 'right'
return dot <= sqlen;
},
pointsSameX: function(p1, p2){
return Math.abs(p1[0] - p2[0]) < eps;
Expand All @@ -71,7 +70,18 @@ function Epsilon(eps){
var dy1 = pt1[1] - pt2[1];
var dx2 = pt2[0] - pt3[0];
var dy2 = pt2[1] - pt3[1];
return Math.abs(dx1 * dy2 - dx2 * dy1) < eps;
var n1 = Math.sqrt(dx1 * dx1 + dy1 * dy1);
var n2 = Math.sqrt(dx2 * dx2 + dy2 * dy2);
// Assuming det(u, v) = 0, we have:
// |det(u + u_err, v + v_err)| = |det(u + u_err, v + v_err) - det(u,v)|
// =|det(u, v_err) + det(u_err. v) + det(u_err, v_err)|
// <= |det(u, v_err)| + |det(u_err, v)| + |det(u_err, v_err)|
// <= N(u)N(v_err) + N(u_err)N(v) + N(u_err)N(v_err)
// <= eps * (N(u) + N(v) + eps)
// We have N(u) ~ N(u + u_err) and N(v) ~ N(v + v_err).
// Assuming eps << N(u) and eps << N(v), we end with:
// |det(u + u_err, v + v_err)| <= eps * (N(u + u_err) + N(v + v_err))
return Math.abs(dx1 * dy2 - dx2 * dy1) <= eps * (n1 + n2);
},
linesIntersect: function(a0, a1, b0, b1){
// returns false if the lines are coincident (e.g., parallel or on top of each other)
Expand All @@ -98,46 +108,44 @@ function Epsilon(eps){
var bdy = b1[1] - b0[1];

var axb = adx * bdy - ady * bdx;
if (Math.abs(axb) < eps)
var n1 = Math.sqrt(adx * adx + ady * ady);
var n2 = Math.sqrt(bdx * bdx + bdy * bdy);
if (Math.abs(axb) <= eps * (n1 + n2))
return false; // lines are coincident

var dx = a0[0] - b0[0];
var dy = a0[1] - b0[1];

var A = (bdx * dy - bdy * dx) / axb;
var B = (adx * dy - ady * dx) / axb;
var pt = [
a0[0] + A * adx,
a0[1] + A * ady
];

var ret = {
alongA: 0,
alongB: 0,
pt: [
a0[0] + A * adx,
a0[1] + A * ady
]
pt: pt
};

// categorize where intersection point is along A and B

if (A <= -eps)
ret.alongA = -2;
else if (A < eps)
if (my.pointsSame(pt, a0))
ret.alongA = -1;
else if (A - 1 <= -eps)
ret.alongA = 0;
else if (A - 1 < eps)
else if (my.pointsSame(pt, a1))
ret.alongA = 1;
else
else if (A < 0)
ret.alongA = -2;
else if (A > 1)
ret.alongA = 2;

if (B <= -eps)
ret.alongB = -2;
else if (B < eps)
if (my.pointsSame(pt, b0))
ret.alongB = -1;
else if (B - 1 <= -eps)
ret.alongB = 0;
else if (B - 1 < eps)
else if (my.pointsSame(pt, b1))
ret.alongB = 1;
else
else if (B < 0)
ret.alongB = -2;
else if (B > 1)
ret.alongB = 2;

return ret;
Expand Down