mpri-graphics-project/MarchingCubes.cpp

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#include "MarchingCubes.hpp"
#include <cassert>
#include <queue>
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#include "GL/gl.h"
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#include "GL/gl.h"
MarchingCubes::MarchingCubes(
const ImplicitSurface& surface,
const Cuboid& box,
double resolution):
surface(surface),
box(box),
resolution(resolution)
{}
MarchingCubes& MarchingCubes::add_hint(const Point& hint) {
hints.push_back(hint);
return *this;
}
Mesh MarchingCubes::operator()() {
Mesh output;
perf_counter = 0;
if(hints.empty())
without_hints(output);
else
with_hints(output);
printf("Explored cubes: %ld\n", perf_counter);
output.translate(surface.getCenter());
return output;
}
void MarchingCubes::without_hints(Mesh& output) {
for(double x = box.low(0); x < box.high(0) + resolution;
x += resolution) {
for(double y = box.low(1); y < box.high(1) + resolution;
y += resolution) {
for(double z = box.low(2); z < box.high(2) + resolution;
z += resolution) {
march_at(x, y, z, output);
perf_counter++;
}
}
}
}
void MarchingCubes::with_hints(Mesh& output) {
std::set<PointLoc> explored_cubes;
std::queue<PointLoc> process;
for(const Point& hint: hints) {
PointLoc coords = coords_of(hint);
PointLoc start_point =
seek_closest_intersection(coords, explored_cubes);
explored_cubes.erase(start_point);
process.push(start_point);
}
while(!process.empty()) {
PointLoc pos = process.front();
process.pop();
if(explored_cubes.find(pos) != explored_cubes.end())
continue;
explored_cubes.insert(pos);
Point pt = point_at_coords(pos);
Intersections inters =
mk_intersection_cube(pt.x, pt.y, pt.z, resolution);
if(!inters.has_inters())
continue;
march_at(pt.x, pt.y, pt.z, output);
for(int dx=-1; dx <= 1; ++dx) {
for(int dy=-1; dy <= 1; ++dy) {
for(int dz=-1; dz <= 1; ++dz) {
if(dx == 0 && dy == 0 && dz == 0)
continue;
PointLoc nPos = pos + PointLoc(dx, dy, dz);
if(coords_in_box(nPos))
process.push(nPos);
}
}
}
}
perf_counter = explored_cubes.size();
}
PointLoc MarchingCubes::seek_closest_intersection(
const PointLoc& loc, std::set<PointLoc>& visited) const {
std::queue<PointLoc> process;
process.push(loc);
while(!process.empty()) {
PointLoc pos = process.front();
process.pop();
if(visited.find(pos) != visited.end())
continue;
visited.insert(pos);
Point pt = point_at_coords(pos);
Intersections inters =
mk_intersection_cube(pt.x, pt.y, pt.z, resolution);
if(inters.has_inters())
return pos;
for(int dx=-1; dx <= 1; ++dx) {
for(int dy=-1; dy <= 1; ++dy) {
for(int dz=-1; dz <= 1; ++dz) {
if(dx == 0 && dy == 0 && dz == 0)
continue;
PointLoc nPos = pos + PointLoc(dx, dy, dz);
if(coords_in_box(nPos))
process.push(nPos);
}
}
}
}
throw SurfaceNotFound();
}
Point MarchingCubes::align_on_bb(const Point& pt) const {
auto align = [resolution = resolution](double v) {
return resolution * floor(v / resolution);
};
Point dist = pt - box.low_pt();
dist.x = align(dist.x);
dist.y = align(dist.y);
dist.z = align(dist.z);
return box.low_pt() + dist;
}
bool MarchingCubes::coords_in_box(const PointLoc& pt) const {
Point low = point_at_coords(pt),
high = point_at_coords(pt + PointLoc(1, 1, 1));
return
low.x >= box.low(0) && low.y >= box.low(1) && low.z >= box.low(2)
&& high.x <= box.high(0) && high.y <= box.high(1)
&& high.z <= box.high(2);
}
PointLoc MarchingCubes::coords_of(const Point& pt) const {
Point dist = pt - box.low_pt();
return PointLoc(
dist.x / resolution,
dist.y / resolution,
dist.z / resolution);
}
Point MarchingCubes::point_at_coords(const PointLoc& coords) const {
return box.low_pt()
+ Point(coords.x * resolution,
coords.y * resolution,
coords.z * resolution);
}
Point MarchingCubes::CubeEdge::at(double pos,
double bx, double by, double bz, double resolution) const
{
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auto bary = [pos](double x, double y) {
return pos * x + (1.-pos) * y;
};
Point p1(
bx + x[0] * resolution,
by + y[0] * resolution,
bz + z[0] * resolution);
Point p2(
bx + x[1] * resolution,
by + y[1] * resolution,
bz + z[1] * resolution);
return Point(
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bary(p1.x, p2.x),
bary(p1.y, p2.y),
bary(p1.z, p2.z));
}
bool MarchingCubes::march_at(double x, double y, double z, Mesh& output) {
/* =====
* NOTE: this code currently computes 8 times the surface value
* at each corner point of the inspected space. This is okay
* for now, because such computations are ultra light and
* actually better than storing values.
* If a time comes when this computation is heavier, because we
* are looking at more complex implicit surfaces,
* IT WILL BE NECESSARY TO ENHANCE THIS CODE!
* ==== */
Intersections intersections = mk_intersection_cube(x, y, z, resolution);
const std::vector<CubeTri>& cur_triangles =
edges_of_intersection[intersections.value()];
for(const CubeTri& cube_tri: cur_triangles) {
Point verts[3] = {
intersect_location(cube_tri.edge[0],
x, y, z),
intersect_location(cube_tri.edge[1],
x, y, z),
intersect_location(cube_tri.edge[2],
x, y, z),
};
size_t vert_ids[3];
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for(int i=0; i < 3; ++i) {
Point normal = surface.normal_at(verts[i]);
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vert_ids[i] = output.add_vertice(verts[i], normal);
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}
for(int i=0; i < 3; ++i) {
output.add_face(
vert_ids[i],
vert_ids[(i+1) % 3],
vert_ids[(i+2) % 3]);
}
}
return !cur_triangles.empty();
}
MarchingCubes::Intersections MarchingCubes::mk_intersection_cube(
double bx, double by, double bz, double side_len) const
{
Intersections intersections;
for(int dx=0; dx <= 1; dx++) {
for(int dy=0; dy <= 1; dy++) {
for(int dz=0; dz <= 1; dz++) {
double cx = bx + side_len * dx;
double cy = by + side_len * dy;
double cz = bz + side_len * dz;
intersections.set_corner(dx, dy, dz,
surface(cx, cy, cz) > 0);
}
}
}
return intersections;
}
Point MarchingCubes::intersect_location(const CubeEdge& edge,
double bx, double by, double bz) const
{
std::function<Point(double, double)> compute =
[&](double low_prop, double high_prop)
{
double med_prop = (low_prop + high_prop) / 2;
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Point med = edge.at(med_prop, bx, by, bz, resolution),
low = edge.at(low_prop, bx, by, bz, resolution),
high = edge.at(high_prop, bx, by, bz, resolution);
if(high_prop - low_prop < 1e-8)
return med;
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double sLow = surface(low),
sMed = surface(med),
sHigh = surface(high);
assert(sLow * sHigh <= 0);
// ^ Can still binary search
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if(sLow * sMed <= 0)
return compute(low_prop, med_prop);
return compute(med_prop, high_prop);
};
return compute(0, 1);
}