flying-balls/polygon_generator.cc

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#include "polygon_generator.h"
#include <cassert>
#include <cmath>
static double to_rad(double angle_in_deg) {
static double PI_180 = M_PI / 180;
return angle_in_deg * PI_180;
}
polygon poly_generate::rectangle(
double width, double height, double mass, std::string label) {
assert(width > 0);
assert(height > 0);
static const double one_over_twelve = 1. / 12;
return polygon{{0, 0},
0,
{{-width / 2, -height / 2},
{-width / 2, height / 2},
{width / 2, height / 2},
{width / 2, -height / 2}},
2023-04-10 14:39:36 +02:00
one_over_twelve * mass * (width * width + height * height),
mass,
label};
}
polygon poly_generate::triangle(
double side1, double side2, double angle, double mass, std::string label) {
assert(side1 > 0);
assert(side2 > 0);
static const double one_over_36 = 1. / 36;
double base, height;
base = side1;
height = side2 * std::sin(to_rad(angle));
vec2d points[] = {
{0, 0}, {side1, 0}, {side2 * std::cos(to_rad(angle)), height}};
vec2d barycenter = {
(points[0].x + points[1].x + points[2].x) / 3,
(points[0].y + points[1].y + points[2].y) / 3,
};
for (unsigned int i = 0; i < 3; ++i)
points[i] -= barycenter;
return polygon{{0, 0},
0,
{std::begin(points), std::end(points)},
one_over_36 * mass * base * std::pow(height, 3),
mass,
label};
}
polygon poly_generate::regular(
double radius, uint n_sides, double mass, std::string label) {
assert(n_sides > 2);
std::vector<vec2d> points;
label += " ";
label += n_sides;
points.reserve(n_sides);
double theta = 2 * M_PI / n_sides;
for (uint i = 0; i < n_sides; i++)
points.push_back({radius * cos(i * theta), radius * sin(i * theta)});
double l = vec2d::norm(points[1] - points[0]);
double sin_, cos_;
sincos(M_PI / n_sides, &sin_, &cos_);
double cot = cos_ / sin_;
double inertia = mass * l * l / 24 * (1 + 3 * cot * cot);
return polygon{{0, 0}, 0, points, inertia, mass, label};
}
static double area_of_triangle(vec2d& a, vec2d& b, vec2d& c) {
return std::abs(vec2d::cross(c - a, b - a)) / 2;
}
static double area_of_poly(std::vector<vec2d>& points, vec2d& centroid) {
double area = 0;
for (int i = 0; i < points.size(); ++i)
area += area_of_triangle(
centroid, points[i], points[(i + 1) % points.size()]);
return area;
}
static double intertia_of_polygon_subtriangle(double total_mass,
double total_area,
vec2d& centroid,
vec2d& p1,
vec2d& p2) {
double partial_area = area_of_triangle(centroid, p1, p2);
double partial_mass = total_mass * partial_area / total_area;
vec2d CA = p1 - centroid;
vec2d AB = p2 - p1;
return partial_mass / 2 *
(vec2d::norm2(AB) / 3 + vec2d::dot(AB, CA) + vec2d::norm2(CA));
}
static vec2d centroid(std::vector<vec2d>& points) {
double x = 0, y = 0;
for (auto& p : points)
x += p.x, y += p.y;
return vec2d{x, y} / points.size();
}
polygon poly_generate::general(
std::vector<vec2d> points, double mass, std::string label) {
double intertia = 0;
vec2d c = centroid(points);
double area = area_of_poly(points, c);
for (int i = 0; i < points.size(); ++i)
intertia += intertia_of_polygon_subtriangle(
mass, area, c, points[i], points[(i + 1) % points.size()]);
for (auto& p : points) // set the center of the polygon to it's centroid
p -= c;
return polygon{{0, 0}, 0, points, intertia, mass, label};
}