WebGL模型拾取——射线法

/*

 */
let Intersector = require(‘./Intersector‘);
let LineSegmentIntersection = require(‘./Intersection‘).LineSegmentIntersection;
let Vec3 = require(‘./Vec3‘);
let Mat4 = require(‘./Mat4‘);
let Algorithm = require(‘./Algorithm‘);

let LineSegmentIntersector = function () {
    Intersector.call(this);

    //原始的起始点和临界值，初始化设置的数据，保留作为参照，设置后不再变动
    this._orginStart = Vec3.new();//线段起点
    this._orginEnd = Vec3.new();//线段终点
    this._orginThreshold = 0.0;//点和线求相交时的临界值，完全相交是很难求到的

    //临时存储，每次求交都可能会变动的数据
    //对于有变换的几何求交，不会变换几何顶点而是变换起始点和临界值
    this._start = Vec3.new();//线段起点
    this._end = Vec3.new();//线段终点
    this._threshold = 0.0;//点和线求相交时的临界值，完全相交是很难求到的

    this._direction = Vec3.new();
    this._length = 0;
    this._inverseLength = 0;
    this._matrix = Mat4.new();
};

LineSegmentIntersector.prototype = Object.create(Intersector.prototype);
LineSegmentIntersector.prototype.constructor = LineSegmentIntersector;
Object.assign(LineSegmentIntersector.prototype, {
    init: function (start, end, threshold) {
        Vec3.copy(this._orginStart, start);
        Vec3.copy(this._orginEnd, end);
        Vec3.copy(this._start, start);
        Vec3.copy(this._end, end);

        if (threshold !== undefined) {
            this._orginThreshold = threshold;
            this._threshold = threshold;
        }
    },
    intersect: function (drawable) {
        //先使用包围盒子
        if (!drawable.getBoundingBox().intersectLineSegment(this._orginStart, this._orginEnd)) {
            return;
        }

        this._drawable = drawable;
        let geometry = drawable.getGeometry();
        let vertexbuffer = geometry.getBufferArray(‘Vertex‘);
        this._vertices = vertexbuffer.getArrayBuffer();
        //没有顶点数据不处理直接返回
        if (!this._vertices) return;

        //没有图元不处理直接返回
        let primitive = geometry.getPrimitive();
        if (!primitive) return;

        //初始化求相交的各种数据
        let matrix = drawable.getTransform();
        if (this._transform !== matrix) {//如果不一样，需要计算新的起始点以及各种临时数据
            this._transform = matrix;
            Mat4.invert(this._matrix, matrix);

            //根据矩阵计算新的临界值
            if (this._orginThreshold > 0.0) {
                let tmp = this._start;
                Mat4.getScale(tmp, this._matrix);
                let x = tmp[0];
                let y = tmp[1];
                let z = tmp[2];
                this._threshold = this._orginThreshold * (x > y ? (x > z ? x : z) : y > z ? y : z);
            }
            //根据矩阵计算新的起始点
            Vec3.transformMat4(this._start, this._orginStart, this._matrix);
            Vec3.transformMat4(this._end, this._orginEnd, this._matrix);

            //根据新的起始点计算各种临时数据
            Vec3.sub(this._direction, this._end, this._start);
            this._length = Vec3.length(this._direction);//长度
            this._inverseLength = this._length <= Algorithm.EPSILON ? 0.0 : 1.0 / this._length;
            Vec3.scale(this._direction, this._direction, this._inverseLength);//求单位向量
        }//如果变换与上次一样，直接使用上次的数据求相交

        //求相交
        primitive.operate(this);
    },
    intersectPoint: function (vertex) {
        // https://www.geometrictools.com/GTEngine/Include/Mathematics/GteDistPointSegment.h
        //起点指向绘制点，向量M
        let m = Vec3.MemoryPool.alloc();
        Vec3.sub(m, vertex, this._start);
        //起点指向终点，向量N
        let n = Vec3.MemoryPool.alloc();
        Vec3.sub(n, this._end, this._start);

        //求M在N上的投影比例值
        //|m|*|n|*cos / \n\*\n\ = |m|*cos/\n\
        let r = Vec3.dot(m, n) * this._inverseLength * this._inverseLength;

        //计算绘制点到线段的距离
        let sqrdist = 1.0;
        if (r < 0.0) {//夹角超过90度，绘制点在当前线段起点后面，求绘制点与起点的距离
            sqrdist = Vec3.sqrLen(m);
        } else if (r > 1.0) {//绘制点在当前线段终点后面，求绘制点与终点的距离
            sqrdist = Vec3.sqrDist(vertex, this._end);
        } else {//在0到1之间
            //m - n * r 如果平行或者接近于平行，结果接近于0，相交
            sqrdist = Vec3.sqrLen(Vec3.scaleAndAdd(m, m, n, -r));
        }

        let intersection = undefined;
        if (sqrdist > this._threshold * this._threshold) {//超过了临界值，没有相交返回

        } else {
            //相交
            intersection = new LineSegmentIntersection();
            //intersection._i1 = index;
            //intersection._r1 = 1.0;
            Vec3.scaleAndAdd(intersection._point, this._start, n, r);
            intersection._ratio = r;
        }
        Vec3.MemoryPool.free(m);
        Vec3.MemoryPool.free(n);
        return intersection;
    },
    intersectLine: function (vertex0, vertex1) {
        // https://www.geometrictools.com/GTEngine/Samples/Geometrics/DistanceSegments3/DistanceSegments3.cpp
        //let epsilon = 0.00000001;

        //起点到终点的向量
        let u = Vec3.MemoryPool.alloc();
        Vec3.sub(u, vertex1, vertex0);
        let v = Vec3.MemoryPool.alloc();
        Vec3.sub(v, this._end, this._start);
        let w = Vec3.MemoryPool.alloc();
        Vec3.sub(w, vertex0, this._start);

        let a = Vec3.dot(u, u);
        let b = Vec3.dot(u, v);
        let c = Vec3.dot(v, v);
        let d = Vec3.dot(u, w);
        let e = Vec3.dot(v, w);
        let D = a * c - b * b;
        let sN;
        let tN;
        let sD = D;
        let tD = D;

        // compute the line parameters of the two closest points
        if (D < Algorithm.EPSILON) {//平行
            // the lines are almost parallel
            sN = 0.0; // force using point P0 on segment S1
            sD = 1.0; // to prevent possible division by 0.0 later
            tN = e;
            tD = c;
        } else {
            // get the closest points on the infinite lines
            sN = b * e - c * d;
            tN = a * e - b * d;
            if (sN < 0.0) {
                // sc < 0 => the s=0 edge is visible
                sN = 0.0;
                tN = e;
                tD = c;
            } else if (sN > sD) {
                // sc > 1  => the s=1 edge is visible
                sN = sD;
                tN = e + b;
                tD = c;
            }
        }

        if (tN < 0.0) {
            // tc < 0 => the t=0 edge is visible
            tN = 0.0;
            // recompute sc for this edge
            if (-d < 0.0) sN = 0.0;
            else if (-d > a) sN = sD;
            else {
                sN = -d;
                sD = a;
            }
        } else if (tN > tD) {
            // tc > 1  => the t=1 edge is visible
            tN = tD;
            // recompute sc for this edge
            if (-d + b < 0.0) sN = 0;
            else if (-d + b > a) sN = sD;
            else {
                sN = -d + b;
                sD = a;
            }
        }
        // finally do the division to get sc and tc
        let sc = Math.abs(sN) < Algorithm.EPSILON ? 0.0 : sN / sD;
        let tc = Math.abs(tN) < Algorithm.EPSILON ? 0.0 : tN / tD;

        // get the difference of the two closest points
        let closest0 = Vec3.MemoryPool.alloc();
        let closest1 = Vec3.MemoryPool.alloc();
        Vec3.scaleAndAdd(closest0, vertex0, u, sc);
        Vec3.scaleAndAdd(closest1, this._start, v, tc);

        let sqrDistance = Vec3.sqrDist(closest0, closest1);
        Vec3.MemoryPool.free(closest0);
        Vec3.MemoryPool.free(closest1);

        let intersection = undefined;
        if (sqrDistance > this._threshold * this._threshold) {

        } else {
            //相交
            intersection = new LineSegmentIntersection();
            // intersection._i1 = index0;
            // intersection._i2 = index1;
            // intersection._r1 = 1.0 - tc;
            // intersection._r2 = tc;
            Vec3.copy(intersection._point, closest1);
            intersection._ratio = tc;
        }
        Vec3.MemoryPool.free(u);
        Vec3.MemoryPool.free(v);
        Vec3.MemoryPool.free(w);
        return intersection;
    },
    intersectTriangle: function (vertex0, vertex1, vertex2) {
        let e2 = Vec3.MemoryPool.alloc();
        Vec3.sub(e2, vertex2, vertex0);
        let e1 = Vec3.MemoryPool.alloc();
        Vec3.sub(e1, vertex1, vertex0);
        let pvec = Vec3.MemoryPool.alloc();
        Vec3.cross(pvec, this._direction, e2);

        let intersection = undefined;
        //线段与三角面点积
        let det = Vec3.dot(pvec, e1);
        //判断三角形所在的平面与线段是否平行，如果平行铁定不相交，面片没有厚度
        if (Math.abs(det) < Algorithm.EPSILON) {
            //return undefined;
        }else{
            let invDet = 1.0 / det;
            let tvec = Vec3.MemoryPool.alloc();
            Vec3.sub(tvec, this._start, vertex0);
            let u = Vec3.dot(pvec, tvec) * invDet;
            //三角面超出了线段两个点范围外面，铁定不相交
            if (u < 0.0 || u > 1.0) {
                //return undefined;
            }else{
                let qvec = Vec3.MemoryPool.alloc();
                Vec3.cross(qvec, tvec, e1);
                let v = Vec3.dot(qvec, this._direction) * invDet;
                //
                if (v < 0.0 || u + v > 1.0) {
                    //return undefined;
                }else{
                    let t = Vec3.dot(qvec, e2) * invDet;
                    if (t < Algorithm.EPSILON || t > this._length) {
                        //return undefined;
                    }else{
                        //相交
                        intersection = new LineSegmentIntersection();

                        //求相交点
                        let r0 = 1.0 - u - v;
                        let r1 = u;
                        let r2 = v;
                        let r = t * this._inverseLength;
                        let interX = vertex0[0] * r0 + vertex1[0] * r1 + vertex2[0] * r2;
                        let interY = vertex0[1] * r0 + vertex1[1] * r1 + vertex2[1] * r2;
                        let interZ = vertex0[2] * r0 + vertex1[2] * r1 + vertex2[2] * r2;
                        // intersection._i1 = index0;
                        // intersection._i2 = index1;
                        // intersection._i3 = index2;
                        // intersection._r1 = r0;
                        // intersection._r2 = r1;
                        // intersection._r3 = r2;

                        //这里的点没有经过变换，不是真实的世界坐标点
                        Vec3.set(intersection._point, interX, interY, interZ);
                        Vec3.transformMat4(intersection._point, intersection._point, this._transform);

                        //求法向量，法向量未变换，如果有用途也要变换
                        let normal = intersection._normal;
                        Vec3.cross(normal, e1, e2);
                        Vec3.normalize(normal, normal);
                        //比例，在相交线段上的比例，不需要变换
                        intersection._ratio = r;
                     }
                }
                Vec3.MemoryPool.free(qvec);
            }
            Vec3.MemoryPool.free(tvec);
        }
        Vec3.MemoryPool.free(e1);
        Vec3.MemoryPool.free(e2);
        Vec3.MemoryPool.free(pvec);
        return intersection;
        // http://gamedev.stackexchange.com/questions/54505/negative-scale-in-matrix-4x4
        // https://en.wikipedia.org/wiki/Determinant#Orientation_of_a_basis
        // you can‘t exactly extract scale of a matrix but the determinant will tell you
        // if the orientation is preserved
        //intersection._backface = mat4.determinant(intersection._matrix) * det < 0;
    },
    intersectBoundingBox: function (box) {
        return box.intersectLineSegment(this._orginStart, this._orginEnd);
    },
});

module.exports = LineSegmentIntersector;


// setDrawable: function (drawable) {
//     this._geometry = drawable.getGeometry();
//     this._vertices = this._geometry.getBufferArray(‘Vertex‘);
//
//     let matrix = drawable.getTransform();
//     if (this._transform === matrix) {//如果与上次的一样，不再处理
//         return;
//     }
//
//     //如果不一样，需要计算新的起始点已经各种临时数据
//     this._transform = matrix;
//     Mat4.invert(this._matrix, matrix);
//
//     //根据矩阵计算新的临界值
//     if (this._orginThreshold > 0.0) {
//         let tmp = this._start;
//         Mat4.getScale(tmp, this._matrix);
//         let x = tmp[0];
//         let y = tmp[1];
//         let z = tmp[2];
//         this._threshold = this._orginThreshold * (x > y ? (x > z ? x : z) : y > z ? y : z);
//     }
//     //根据矩阵计算新的起始点
//     Vec3.transformMat4(this._start, this._orginStart, this._matrix);
//     Vec3.transformMat4(this._end, this._orginEnd, this._matrix);
//
//     //根据新的起始点计算各种临时数据
//     Vec3.sub(this._direction, this._end, this._start);
//     this._length = Vec3.length(this._direction);//长度
//     this._inverseLength = this._length <= Algorithm.EPSILON ? 1.0 / this._length : 0.0;
//     Vec3.scale(this._direction, this._direction, this._inverseLength);//求单位向量
// },
// setGeometry: function (geometry, matrix) {
//     Intersector.prototype.setGeometry.call(this, geometry, matrix);
//
//     //如果不一样，需要计算新的起始点已经各种临时数据
//     Mat4.invert(this._matrix, matrix);
//
//     //根据矩阵计算新的临界值
//     if (this._orginThreshold > 0.0) {
//         let tmp = this._start;
//         Mat4.getScale(tmp, this._matrix);
//         let x = tmp[0];
//         let y = tmp[1];
//         let z = tmp[2];
//         this._threshold = this._orginThreshold * (x > y ? (x > z ? x : z) : y > z ? y : z);
//     }
//     //根据矩阵计算新的起始点
//     Vec3.transformMat4(this._start, this._orginStart, this._matrix);
//     Vec3.transformMat4(this._end, this._orginEnd, this._matrix);
//
//     //根据新的起始点计算各种临时数据
//     Vec3.sub(this._direction, this._end, this._start);
//     this._length = Vec3.length(this._direction);//长度
//     this._inverseLength = this._length <= Algorithm.EPSILON ? 1.0 / this._length : 0.0;
//     Vec3.scale(this._direction, this._direction, this._inverseLength);//求单位向量
// },
// setGeometry: function (geometry) {
//     //没有顶点数据不处理直接返回
//     let vertexbuffer = geometry.getBufferArray(‘Vertex‘);
//     if(!vertexbuffer) return;
//
//     //没有图元不处理直接返回
//     let primitive = geometry.getPrimitive();
//     if (primitive)
//         primitive.operate(this);
// },