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4a288a7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | // @flow
import {vec3, vec4} from 'gl-matrix';
import assert from 'assert';
class Frustum {
points: Array<Array<number>>;
planes: Array<Array<number>>;
constructor(points_: Array<Array<number>>, planes_: Array<Array<number>>) {
this.points = points_;
this.planes = planes_;
}
static fromInvProjectionMatrix(invProj: Float64Array, worldSize: number, zoom: number): Frustum {
const clipSpaceCorners = [
[-1, 1, -1, 1],
[ 1, 1, -1, 1],
[ 1, -1, -1, 1],
[-1, -1, -1, 1],
[-1, 1, 1, 1],
[ 1, 1, 1, 1],
[ 1, -1, 1, 1],
[-1, -1, 1, 1]
];
const scale = Math.pow(2, zoom);
// Transform frustum corner points from clip space to tile space
const frustumCoords = clipSpaceCorners
.map(v => vec4.transformMat4([], v, invProj))
.map(v => vec4.scale([], v, 1.0 / v[3] / worldSize * scale));
const frustumPlanePointIndices = [
[0, 1, 2], // near
[6, 5, 4], // far
[0, 3, 7], // left
[2, 1, 5], // right
[3, 2, 6], // bottom
[0, 4, 5] // top
];
const frustumPlanes = frustumPlanePointIndices.map((p: Array<number>) => {
const a = vec3.sub([], frustumCoords[p[0]], frustumCoords[p[1]]);
const b = vec3.sub([], frustumCoords[p[2]], frustumCoords[p[1]]);
const n = vec3.normalize([], vec3.cross([], a, b));
const d = -vec3.dot(n, frustumCoords[p[1]]);
return n.concat(d);
});
return new Frustum(frustumCoords, frustumPlanes);
}
}
class Aabb {
min: vec3;
max: vec3;
center: vec3;
constructor(min_: vec3, max_: vec3) {
this.min = min_;
this.max = max_;
this.center = vec3.scale([], vec3.add([], this.min, this.max), 0.5);
}
quadrant(index: number): Aabb {
const split = [(index % 2) === 0, index < 2];
const qMin = vec3.clone(this.min);
const qMax = vec3.clone(this.max);
for (let axis = 0; axis < split.length; axis++) {
qMin[axis] = split[axis] ? this.min[axis] : this.center[axis];
qMax[axis] = split[axis] ? this.center[axis] : this.max[axis];
}
// Elevation is always constant, hence quadrant.max.z = this.max.z
qMax[2] = this.max[2];
return new Aabb(qMin, qMax);
}
distanceX(point: Array<number>): number {
const pointOnAabb = Math.max(Math.min(this.max[0], point[0]), this.min[0]);
return pointOnAabb - point[0];
}
distanceY(point: Array<number>): number {
const pointOnAabb = Math.max(Math.min(this.max[1], point[1]), this.min[1]);
return pointOnAabb - point[1];
}
// Performs a frustum-aabb intersection test. Returns 0 if there's no intersection,
// 1 if shapes are intersecting and 2 if the aabb if fully inside the frustum.
intersects(frustum: Frustum): number {
// Execute separating axis test between two convex objects to find intersections
// Each frustum plane together with 3 major axes define the separating axes
// Note: test only 4 points as both min and max points have equal elevation
assert(this.min[2] === 0 && this.max[2] === 0);
const aabbPoints = [
[this.min[0], this.min[1], 0.0, 1],
[this.max[0], this.min[1], 0.0, 1],
[this.max[0], this.max[1], 0.0, 1],
[this.min[0], this.max[1], 0.0, 1]
];
let fullyInside = true;
for (let p = 0; p < frustum.planes.length; p++) {
const plane = frustum.planes[p];
let pointsInside = 0;
for (let i = 0; i < aabbPoints.length; i++) {
pointsInside += vec4.dot(plane, aabbPoints[i]) >= 0;
}
if (pointsInside === 0)
return 0;
if (pointsInside !== aabbPoints.length)
fullyInside = false;
}
if (fullyInside)
return 2;
for (let axis = 0; axis < 3; axis++) {
let projMin = Number.MAX_VALUE;
let projMax = -Number.MAX_VALUE;
for (let p = 0; p < frustum.points.length; p++) {
const projectedPoint = frustum.points[p][axis] - this.min[axis];
projMin = Math.min(projMin, projectedPoint);
projMax = Math.max(projMax, projectedPoint);
}
if (projMax < 0 || projMin > this.max[axis] - this.min[axis])
return 0;
}
return 1;
}
}
export {
Aabb,
Frustum
};
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