问题
I wrote map editor to my platform game. I'm using SFML. Map consists of polygons - ConvexShapes. I need to add selection of ConvexShapes by clicking on them. I know that I can use cv.getLocalBounds() to obtain rectangle and next check that but I need more precise solution. How to check if clicked point belongs to any shape?
回答1:
Based on question comments link, this is what I got.
Using the algorithm described there, we could determine if a given point is inside a shape counting how many crossing points are on each side
If the number of them are odd on each side, the point belongs to the shape. Easy then:
bool contains(sf::ConvexShape shape, sf::Vector2f point){
std::vector<sf::Vector2f> intersectPoints = getIntersectionPoints(shape, point);
int nodesAtLeft = 0;
int nodesAtRight = 0;
for (sf::Vector2f po : intersectPoints){
if (po.x < point.x){
nodesAtLeft++;
}
else if(po.x > point.x){
nodesAtRight++;
}
}
return ((nodesAtLeft % 2) == 1) && ((nodesAtRight % 2) == 1);
}
So, how do we get those intersection points? We should check for each side of the shape where is the crossing point with the horizontal line determined by our given point. Note that the crossing point could be far away from the shape, due to calculation of the crossing point consider whole lines, not segments
So, once we have got that crossing point, we should check if it belongs to the segment.
std::vector<sf::Vector2f> getIntersectionPoints(sf::ConvexShape shape, sf::Vector2f point){
std::vector<sf::Vector2f> intersectPoints;
sf::Vector2f p;
bool crossingLine; // This will be used to avoid duplicated points on special cases
if (shape.getPointCount() < 3){
return intersectPoints;
}
sf::FloatRect bounds = shape.getLocalBounds();
// To determine horizontal line, we use two points, one at leftmost side of the shape (in fact, its bound) and the other at rightmost side
Line pointLine, shapeLine;
pointLine.p1 = sf::Vector2f(bounds.left, point.y);
pointLine.p2 = sf::Vector2f(bounds.left + bounds.width, point.y);
unsigned int nPoints = shape.getPointCount();
for (int i = 0; i < nPoints; ++i){
try{
shapeLine.p1 = shape.getPoint(i % nPoints); // Last one will be nPoints-1
shapeLine.p2 = shape.getPoint((i + 1) % nPoints); // So this one must be 0 in order to check last side (returning to origin)
crossingLine = (shapeLine.p1.y >= point.y && shapeLine.p2.y <= point.y) || (shapeLine.p2.y >= point.y && shapeLine.p1.y <= point.y);
p = intersection(shapeLine, pointLine);
if (crossingLine && shapeLine.contains(p))
intersectPoints.push_back(p);
}
catch (std::runtime_error e){
}
}
return intersectPoints;
}
I think the easiest way to check if a point C belongs to a segment (defined by points A and B) is by doing a distance check like:
distance(A,C) + distance(C,B) == distance(A,B)
But as this one could end being too restrictive, I've adapted it to consider a little error margin:
abs((distance(A, C) + distance(C, B)) - distance(A, B)) < margin
Before I forget, this is how a Line is defined
struct Line{
sf::Vector2f p1;
sf::Vector2f p2;
bool contains(sf::Vector2f point) const{
float margin = 0.1;
return std::abs((distance(p1, point) + distance(point, p2)) - distance(p1, p2)) < margin;
}
};
With this, the only thing left now is to calculate the intersection points between two given lines. Sincerely, I'm not going to explain this (mainly because I've just copied this from wikipedia)
sf::Vector2f intersection(Line lineA, Line lineB){
int x1 = lineA.p1.x;
int y1 = lineA.p1.y;
int x2 = lineA.p2.x;
int y2 = lineA.p2.y;
int x3 = lineB.p1.x;
int y3 = lineB.p1.y;
int x4 = lineB.p2.x;
int y4 = lineB.p2.y;
try{
double retX = ((x1*y2 - y1*x2)*(x3 - x4) - (x1 - x2)*(x3*y4 - y3*x4)) / ((x1 - x2)*(y3 - y4) - (y1 - y2)*(x3 - x4));
double retY = ((x1*y2 - y1*x2)*(y3 - y4) - (y1 - y2)*(x3*y4 - y3*x4)) / ((x1 - x2)*(y3 - y4) - (y1 - y2)*(x3 - x4));
return sf::Vector2f(retX, retY);
}
catch (std::exception){
throw new std::exception("");
}
}
If the lines are parallel or the same line, both denominators are zero, and it will throw an DivideByZero exception, not really a problem simply there is not intersection.
I've made also a snippet to test this:
int main()
{
sf::RenderWindow v(sf::VideoMode(600,400), "SFML");
sf::ConvexShape shape;
std::vector<sf::Vector2i> points;
std::vector<sf::CircleShape> intPoints;
shape.setPointCount(0);
shape.setOutlineColor(sf::Color::Blue);
shape.setFillColor(sf::Color::Black);
shape.setOutlineThickness(1);
while (v.isOpen()){
sf::Event event;
while (v.pollEvent(event)){
if (event.type == sf::Event::Closed)
v.close();
else if (event.type == sf::Event::MouseButtonPressed){
if (event.mouseButton.button == sf::Mouse::Button::Left){
// Add a point to the shape
intPoints.clear();
sf::Vector2i p = sf::Mouse::getPosition(v);
points.push_back(p);
shape.setPointCount(points.size());
for (int i = 0; i < points.size(); ++i){
shape.setPoint(i, sf::Vector2f(points[i]));
}
}
else if (event.mouseButton.button == sf::Mouse::Button::Right){
// Delete shape
points.clear();
intPoints.clear();
shape.setPointCount(0);
}
else if (event.mouseButton.button == sf::Mouse::Button::Middle){
// Set testing point
intPoints.clear();
sf::Vector2i p = sf::Mouse::getPosition(v);
if (contains(shape, sf::Vector2f(p))){
std::cout << "Point inside shape" << std::endl;
}
else{
std::cout << "Point outside shape" << std::endl;
}
auto v = getIntersectionPoints(shape, sf::Vector2f(p));
for (sf::Vector2f po : v){
sf::CircleShape c(2);
c.setFillColor(sf::Color::Green);
c.setOrigin(1, 1);
c.setPosition(po);
intPoints.push_back(c);
}
// testing point added too, to be visualized
sf::CircleShape c(2);
c.setFillColor(sf::Color::Red);
c.setOrigin(1, 1);
c.setPosition(sf::Vector2f(p));
intPoints.push_back(c);
}
}
}
v.clear();
v.draw(shape);
for (sf::CircleShape c : intPoints){
v.draw(c);
}
v.display();
}
return 0;
}
Some captures:
May be a long post, but I've tried to be clear.
来源：https://stackoverflow.com/questions/38535430/how-to-check-if-point-belongs-to-convexshape