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Polygon.h
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Polygon.h
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#ifndef POLYGON_H
#define POLYGON_H
#include "Shape.h"
class Object;
class Polygon : public Shape {
friend class Physics;
private:
int nPoints;
vector<Vector2D> points, normals, curPoints, curNormals;
double GetCutLengthX(double x) {
double minI = -DBL_INF, maxI = DBL_INF;
Line cutLine(Vector2D(x, 0, 1), Vector2D(x, 1, 1));
for (int i = 0; i < nPoints; i++) {
Line edge(points[i], points[(i + 1) % nPoints]);
if (sgn(edge.v.x) == 0) continue;
else {
double c = (edge * cutLine).y;
if (sgn(edge.v.x) < 0) {
maxI = min(maxI, c);
} else {
minI = max(minI, c);
}
}
}
return maxI - minI;
}
double GetCutLengthY(double y) {
double minI = -DBL_INF, maxI = DBL_INF;
Line cutLine(Vector2D(0, y, 1), Vector2D(1, y, 1));
for (int i = 0; i < nPoints; i++) {
Line edge(points[i], points[(i + 1) % nPoints]);
if (sgn(edge.v.y) == 0) continue;
else {
double c = (edge * cutLine).x;
if (sgn(edge.v.y) > 0) {
maxI = min(maxI, c);
} else {
minI = max(minI, c);
}
}
}
return maxI - minI;
}
public:
static const int ShapeType = 0;
static const double GearD;
Polygon() : Shape() {
nPoints = 0;
}
Polygon(Vector2D *begin, Vector2D *end) {
nPoints = end - begin;
points = vector<Vector2D>(begin, end);
Update();
curPoints.resize(nPoints);
curNormals.resize(nPoints);
for (int i = 0; i < nPoints; i++)
normals.push_back((points[loopNext(i, nPoints)] - points[i]).GetInverseRotate().GetDirection());
}
Polygon(vector<Vector2D> points) : Shape() {
nPoints = (int)points.size();
this->points = points;
Update();
curPoints.resize(nPoints);
curNormals.resize(nPoints);
for (int i = 0; i < nPoints; i++)
normals.push_back((points[loopNext(i, nPoints)] - points[i]).GetInverseRotate().GetDirection());
}
void Move(Vector2D vec) {
for (int i = 0; i < (int)points.size(); i++)
points[i] += vec;
Update();
}
void Redraw() {
graphics.DrawPolygon(curPoints, color, boundaryWidth);
}
const Vector2D &GetNormal(int i) const {
return curNormals[i];
}
Vector2D GetLowestPoint(Vector2D normal) {
double lowest = DBL_INF;
Vector2D ret;
for (int i = 0; i < nPoints; i++) {
double prod = normal * curPoints[i];
if (prod < lowest) {
ret = curPoints[i];
lowest = prod;
}
}
return ret;
}
const Vector2D &GetPoint(int i) const{
return curPoints[i];
}
const Line GetEdge(int i) const {
return Line(GetPoint(i), GetPoint(loopNext(i, nPoints)));
}
bool IsPointInside(Vector2D p) const {
p = GetTransformToWorldInverse()(p);
for (int i = 0; i < nPoints; i++)
if (sgn((p - points[i]) % (points[loopNext(i, nPoints)] - points[i])) > 0) return false;
return true;
}
double CalcMass() {
double ret = 0;
for (int i = 0; i < nPoints; i++)
ret += points[i] % points[loopNext(i, nPoints)];
ret *= density / 2;
return ret;
}
void ResetCentroid() {
mass = CalcMass();
Vector2D newCenter = Vector2D(0, 0, 0);
for (int i = 0; i < nPoints; i++)
newCenter += (points[i] + points[(i + 1) % nPoints]) * (points[i] % points[(i + 1) % nPoints]) / 2;
newCenter /= (mass / density) * 3;
newCenter.z = 0;
centroidPosition = newCenter;
}
double CalcInertia() {
double ret = 0;
vector<double> xList, yList;
for (int i = 0; i < nPoints; i++) xList.push_back(points[i].x), yList.push_back(points[i].y);
sort(xList.begin(), xList.end());
sort(yList.begin(), yList.end());
for (int i = 0; i < nPoints - 1; i++) {
double x0 = xList[i], x3 = xList[i + 1];
double x1 = x0 + (x3 - x0) / 3, x2 = x0 + (x3 - x0) / 3 * 2;
ret += (GetCutLengthX(x0) * x0 * x0 +
GetCutLengthX(x1) * x1 * x1 * 3 +
GetCutLengthX(x2) * x2 * x2 * 3 +
GetCutLengthX(x3) * x3 * x3) / 8.0 * (x3 - x0);
}
for (int i = 0; i < nPoints - 1; i++) {
double y0 = yList[i], y3 = yList[i + 1];
double y1 = y0 + (y3 - y0) / 3, y2 = y0 + (y3 - y0) / 3 * 2;
ret += (GetCutLengthY(y0) * y0 * y0 +
GetCutLengthY(y1) * y1 * y1 * 3 +
GetCutLengthY(y2) * y2 * y2 * 3 +
GetCutLengthY(y3) * y3 * y3) / 8.0 * (y3 - y0);
}
return ret;
}
void ResetDirection() {
bool isCW = false, isCCW = false;
for (int i = 0; i < nPoints; i++) {
Vector2D a = points[(i + 1) % nPoints] - points[i],
b = points[(i + 2) % nPoints] - points[(i + 1) % nPoints];
int t = sgn(a % b);
if (t > 0) isCCW = true;
if (t < 0) isCW = true;
}
if (isCCW && isCW) {
printf("Warning : Polygon non-convex!!!\n");
}
if (isCW) reverse(points.begin(), points.end());
}
void Update() {
ResetDirection();
ResetCentroid();
inertia = CalcInertia();
}
void GetProjection(const Vector2D &normal, double &minI, double &maxI) {
assert(nPoints);
minI = maxI = GetPoint(0) * normal;
for (int i = 1; i < nPoints; i++) {
double prod = curPoints[i] * normal;
if (prod < minI) minI = prod;
if (prod > maxI) maxI = prod;
}
}
static Polygon *GeneratePolygon(int nPoints, double r) {
vector<Vector2D> points;
points.resize(nPoints);
for (int i = 0; i < nPoints; i++)
points[i] = Vector2D::Origin + r * Vector2D::RotatedUnitVector(-pi / 2 + pi / nPoints + 2 * pi / nPoints * i);
Polygon *poly = new Polygon(points);
return poly;
}
int GetType() {
return ShapeType;
}
static Polygon *GenerateBox(double w, double h) {
Vector2D points[4];
w /= 2; h /= 2;
points[0] = Vector2D(-w, -h, 1);
points[1] = Vector2D(w, -h, 1);
points[2] = Vector2D(w, h, 1);
points[3] = Vector2D(-w, h, 1);
Polygon *poly = new Polygon(points, points + 4);
return poly;
}
static vector<Vector2D> GenerateGearPoints(Vector2D center, double r, double rad) {
double d = 14, R = r;
int n = (int)ceil(2 * pi / rad);
rad = 2 * pi / n;
vector<Vector2D> points;
for (int i = 0; i < n; i++) {
points.push_back(center + Vector2D::RotatedUnitVector(i * rad + 0.000 * rad) * (R - d));
points.push_back(center + Vector2D::RotatedUnitVector(i * rad + 0.250 * rad) * (R - d));
points.push_back(center + Vector2D::RotatedUnitVector(i * rad + 0.525 * rad) * (R + d));
points.push_back(center + Vector2D::RotatedUnitVector(i * rad + 0.725 * rad) * (R + d));
}
return points;
}
AABB GetAABB() {
AABB ret;
GetProjection(Vector2D(1, 0, 0), ret.x0, ret.x1);
GetProjection(Vector2D(0, 1, 0), ret.y0, ret.y1);
return ret;
}
void UpdateCurrentInformation();
};
#endif