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export var epsilon = 1e-10;
export function epsilonesque(n) {
return n <= epsilon && n >= -epsilon;
}
// IN: vectors or vertices
// OUT: dot product
export function dot(v0, v1) {
return v0.x * v1.x + v0.y * v1.y + v0.z * v1.z;
}
// IN: two vertex objects, v0 and v1
// OUT: true if they are linearly dependent, false otherwise
// from https://math.stackexchange.com/questions/1144357/how-can-i-prove-that-two-vectors-in-%E2%84%9D3-are-linearly-independent-iff-their-cro
export function linearDependent(v0, v1) {
return (
epsilonesque(v0.x * v1.y - v0.y * v1.x) &&
epsilonesque(v0.y * v1.z - v0.z * v1.y) &&
epsilonesque(v0.z * v1.x - v0.x * v1.z)
);
}
// IN: an array of 2D-points [x,y]
// OUT: true if the set defines a convex polygon (non-intersecting, hole-free, non-concave)
// from https://gist.github.com/annatomka/82715127b74473859054, adapted to [x,y] syntax (instead of {x: ..., y: ...}) and optimizations
export function polygonDirection(polygon) {
var sign, crossproduct, p0, p1, p2, v0, v1, i;
//begin: initialization
p0 = polygon[polygon.length - 2];
p1 = polygon[polygon.length - 1];
p2 = polygon[0];
v0 = vect(p0, p1);
v1 = vect(p1, p2);
crossproduct = calculateCrossproduct(v0, v1);
// console.log(`[[${p0}], [${p1}], [${p2}]] => (${v0}) x (${v1}) = ${crossproduct}`);
sign = Math.sign(crossproduct);
//end: initialization
p0 = p1; // p0 = polygon[polygon.length - 1];
p1 = p2; // p1 = polygon[0];
p2 = polygon[1];
v0 = v1;
v1 = vect(p1, p2);
crossproduct = calculateCrossproduct(v0, v1);
// console.log(`[[${p0}], [${p1}], [${p2}]] => (${v0}) x (${v1}) = ${crossproduct}`);
if (Math.sign(crossproduct) !== sign) {
return undefined;
} //different signs in cross products means concave polygon
//iterate on remaining 3 consecutive points
for (i = 2; i < polygon.length - 1; i++) {
p0 = p1;
p1 = p2;
p2 = polygon[i];
v0 = v1;
v1 = vect(p1, p2);
crossproduct = calculateCrossproduct(v0, v1);
// console.log(`[[${p0}], [${p1}], [${p2}]] => (${v0}) x (${v1}) = ${crossproduct}`);
if (Math.sign(crossproduct) !== sign) {
return undefined;
} //different signs in cross products means concave polygon
}
return sign;
}
function vect(from, to) {
return [to[0] - from[0], to[1] - from[1]];
}
function calculateCrossproduct(v0, v1) {
return v0[0] * v1[1] - v0[1] * v1[0];
}