static void cylinder_intersect(cylinder * cyl, ray * ry) {
vector rc, n, D, O;
flt t, s, tin, tout, ln, d;
rc.x = ry->o.x - cyl->ctr.x;
rc.y = ry->o.y - cyl->ctr.y;
rc.z = ry->o.z - cyl->ctr.z;
VCross(&ry->d, &cyl->axis, &n);
VDOT(ln, n, n);
ln=sqrt(ln); /* finish length calculation */
if (ln == 0.0) { /* ray is parallel to the cylinder.. */
VDOT(d, rc, cyl->axis);
D.x = rc.x - d * cyl->axis.x;
D.y = rc.y - d * cyl->axis.y;
D.z = rc.z - d * cyl->axis.z;
VDOT(d, D, D);
d = sqrt(d);
tin = -FHUGE;
tout = FHUGE;
/* if (d <= cyl->rad) then ray is inside cylinder.. else outside */
}
VNorm(&n);
VDOT(d, rc, n);
d = fabs(d);
if (d <= cyl->rad) { /* ray intersects cylinder.. */
VCross(&rc, &cyl->axis, &O);
VDOT(t, O, n);
t = - t / ln;
VCross(&n, &cyl->axis, &O);
VNorm(&O);
VDOT(s, ry->d, O);
s = fabs(sqrt(cyl->rad*cyl->rad - d*d) / s);
tin = t - s;
add_intersection(tin, (object *) cyl, ry);
tout = t + s;
add_intersection(tout, (object *) cyl, ry);
}
}
static void plane_intersect(plane * pln, ray * ry) {
flt t,td;
t=-(pln->d + VDot(&pln->norm, &ry->o));
td=VDot(&pln->norm, &ry->d);
if (td != 0.0) {
t /= td;
if (t > 0.0)
add_intersection(t,(object *) pln, ry);
}
}
static void sphere_intersect(sphere * spr, ray * ry) {
flt b, disc, t1, t2, temp;
vector V;
VSUB(spr->ctr, ry->o, V);
VDOT(b, V, ry->d);
VDOT(temp, V, V);
disc=b*b + spr->rad*spr->rad - temp;
if (disc<=0.0) return;
disc=sqrt(disc);
t2=b+disc;
if (t2 <= SPEPSILON)
return;
add_intersection(t2, (object *) spr, ry);
t1=b-disc;
if (t1 > SPEPSILON)
add_intersection(t1, (object *) spr, ry);
}
static int intersect_line_segment(TTF_Segment *segment, TTF_Scan_Line *scanline) {
if (!segment || !scanline) {
return 0;
}
float y = scanline->y;
float x0 = segment->x[0], x1 = segment->x[1];
float y0 = segment->y[0], y1 = segment->y[1];
if ((fabsf(y - y0) + fabsf(y - y1) - fabsf(y1 - y0)) != 0) {
/* The scan-line at y is not within the y-bounds of the line segment. */
return 0;
}
if (y0 == y1) {
/* Intersecting with horizontal line (degenerate case). */
if (y == y0) {
/* There are two intersections, x0 and x1. */
add_intersection(scanline, x0);
add_intersection(scanline, x1);
return 2;
} else {
/* No intersections. */
return 0;
}
}
/* Calculate x-intersection of scan-line and line segment. */
float x = ((x0*y1 - x1*y0) + y*(x1 - x0)) / (y1 - y0);
if ((fabsf(x - x0) + fabsf(x - x1) - fabsf(x1 - x0)) != 0) {
/* The x-intersection is not within the x-bounds of the line segment. */
return 0;
}
add_intersection(scanline, x);
return 1;
}
typename enable_if<is_concept_combinable<is_interval_map, is_interval_set, Type, KeySetT>, void>::type
add_intersection(Type& section, const Type& object, const KeySetT& key_set)
{
typedef typename KeySetT::const_iterator const_iterator;
if(icl::is_empty(key_set))
return;
const_iterator common_lwb, common_upb;
if(!Set::common_range(common_lwb, common_upb, key_set, object))
return;
const_iterator it_ = common_lwb;
while(it_ != common_upb)
add_intersection(section, object, *it_++);
}
/* Returns the intersection points between the particle trajectory
* and the domain boundaries
* intersections are placed in increasing x position
*/
std::vector<bpoint> boundaries_intersections(Line line) {
std::vector<bg::model::segment<bpoint> > segments = get_geometry_segments();
//std::vector<bg::model::segment<bpoint> > segments = get_geometry_segments();
//Compute intersections with all segments of detector boundary
std::vector<bpoint> intersections;
for (unsigned i = 0; i < segments.size(); i++) {
add_intersection(line, segments[i], intersections);
}
Utils::sort_points_by_coord(&intersections);
intersections = Utils::unique_bpoints(intersections);
//unique(intersections.begin(), intersections.end());
//intersections.erase(unique(intersections.begin(), intersections.end()),
// intersections.end());
//intersections.shrink_to_fit();
return intersections;
}
static void ring_intersect(ring * rng, ray * ry) {
flt d;
flt t,td;
vector hit, pnt;
d = -VDot(&(rng->ctr), &(rng->norm));
t=-(d+VDot(&(rng->norm), &(ry->o)));
td=VDot(&(rng->norm),&(ry->d));
if (td != 0.0) {
t= t / td;
if (t>=0.0) {
hit=Raypnt(ry, t);
VSUB(hit, rng->ctr, pnt);
VDOT(td, pnt, pnt);
td=sqrt(td);
if ((td > rng->inrad) && (td < rng->outrad))
add_intersection(t,(object *) rng, ry);
}
}
}
typename enable_if
<
mpl::and_< mpl::not_<is_total<Type> >
, is_concept_compatible<is_interval_map, Type, MapT> >
, void
>::type
add_intersection(Type& section, const Type& object, const MapT& operand)
{
typedef typename Type::segment_type segment_type;
typedef typename Type::interval_type interval_type;
typedef typename MapT::const_iterator const_iterator;
if(operand.empty())
return;
const_iterator common_lwb, common_upb;
if(!Set::common_range(common_lwb, common_upb, operand, object))
return;
const_iterator it_ = common_lwb;
while(it_ != common_upb)
add_intersection(section, object, *it_++);
}
static void tri_intersect(tri * trn, ray * ry) {
vector tvec, pvec, qvec;
flt det, inv_det, t, u, v;
/* begin calculating determinant - also used to calculate U parameter */
CROSS(pvec, ry->d, trn->edge2);
/* if determinant is near zero, ray lies in plane of triangle */
det = DOT(trn->edge1, pvec);
if (det > -EPSILON && det < EPSILON)
return;
inv_det = 1.0 / det;
/* calculate distance from vert0 to ray origin */
SUB(tvec, ry->o, trn->v0);
/* calculate U parameter and test bounds */
u = DOT(tvec, pvec) * inv_det;
if (u < 0.0 || u > 1.0)
return;
/* prepare to test V parameter */
CROSS(qvec, tvec, trn->edge1);
/* calculate V parameter and test bounds */
v = DOT(ry->d, qvec) * inv_det;
if (v < 0.0 || u + v > 1.0)
return;
/* calculate t, ray intersects triangle */
t = DOT(trn->edge2, qvec) * inv_det;
add_intersection(t,(object *) trn, ry);
}
int main()
{
std::scanf("%d", &n);
rotate_sin = sinl(233.3);
rotate_cos = cosl(233.3);
for(int i = 0; i != n; ++i)
{
for(int j = 0; j != 3; ++j)
{
std::scanf("%Lf %Lf", &pt[i][j].x, &pt[i][j].y);
pt[i][j] = rotate(pt[i][j]);
coordinate[tot++] = pt[i][j].y;
}
for(int j = 0; j != i; ++j)
{
add_intersection(i, 0, 1, j, 0, 1);
add_intersection(i, 0, 1, j, 0, 2);
add_intersection(i, 0, 1, j, 1, 2);
add_intersection(i, 0, 2, j, 0, 1);
add_intersection(i, 0, 2, j, 0, 2);
add_intersection(i, 0, 2, j, 1, 2);
add_intersection(i, 1, 2, j, 0, 1);
add_intersection(i, 1, 2, j, 0, 2);
add_intersection(i, 1, 2, j, 1, 2);
}
}
std::sort(coordinate, coordinate + tot);
tot = std::unique(coordinate, coordinate + tot, cmp) - coordinate;
long double area = 0.0, prev_len = 0.0;
for(int i = 0; i != tot; ++i, num = 0)
{
long double y = coordinate[i];
for(int j = 0; j != n; ++j)
{
if(add_horizontal(y, j, 0, 1)) continue;
if(add_horizontal(y, j, 0, 2)) continue;
if(add_horizontal(y, j, 1, 2)) continue;
long double d1 = get_intersection(y, pt[j][0], pt[j][1]);
long double d2 = get_intersection(y, pt[j][0], pt[j][2]);
long double d3 = get_intersection(y, pt[j][1], pt[j][2]);
add_segment(d2, d3);
add_segment(d1, d3);
add_segment(d1, d2);
}
std::sort(data, data + num);
int cnt = 0;
long double prev = 0.0, len = 0.0;
for(int j = 0; j != num; ++j)
{
if(!cnt) prev = data[j].x;
cnt += data[j].cnt;
if(!cnt) len += data[j].x - prev;
}
if(i) area += (len + prev_len) * (y - coordinate[i - 1]) * (long double)0.5;
prev_len = len;
}
std::printf("%.2Lf\n", area);
return 0;
}
static int intersect_curve_segment(TTF_Segment *segment, TTF_Scan_Line *scanline) {
if (!segment || !scanline) {
return 0;
}
float t;
float y = scanline->y;
float y0 = segment->y[0], y1 = segment->y[1], y2 = segment->y[2];
float x0 = segment->x[0], x1 = segment->x[1], x2 = segment->x[2];
float a = y0 - 2*y1 + y2;
float b = 2*y1 - 2*y0;
float c = y0 - y;
/* Handle degenerate cases first. */
if (a == 0) {
/* Curve is a straight line. */
if (b == 0) {
/* Curve is a horizontal line. */
if (c == 0) {
/* There are two intersections, x0 and x2. */
add_intersection(scanline, x0);
add_intersection(scanline, x2);
return 2;
} else {
/* No intersections. */
return 0;
}
} else {
t = -c / b;
if (IN(t, 0.0, 1.0)) {
/* One intersection. */
add_intersection(scanline, quad_bezier(t, x0, x1, x2));
return 1;
} else {
/* No intersections. */
return 0;
}
}
}
/* Test discriminant for number of roots. */
float D = b*b - 4*a*c;
if (D < 0) {
/* No roots. */
return 0;
} else if (D == 0) {
/* One distinct root. */
t = -b / (2*a);
if (IN(t, 0.0, 1.0)) {
/* One intersection. */
add_intersection(scanline, quad_bezier(t, x0, x1, x2));
return 1;
} else {
/* No intersections. */
return 0;
}
} else {
/* Two distinct roots. */
int num_intersections = 0;
t = (-b + sqrt(D)) / (2*a);
if (IN(t, 0.0, 1.0)) {
/* Intersection point is within curve endpoints. */
add_intersection(scanline, quad_bezier(t, x0, x1, x2));
num_intersections++;
}
t = (-b - sqrt(D)) / (2*a);
if (IN(t, 0.0, 1.0)) {
/* Intersection point is within curve endpoints. */
add_intersection(scanline, quad_bezier(t, x0, x1, x2));
num_intersections++;
}
return num_intersections;
}
}