如何分辨圆和矩形在二维欧几里得空间中是否相交?(即经典二维几何)
当前回答
有效,一周前才发现,现在才开始测试。
double theta = Math.atan2(cir.getX()-sqr.getX()*1.0,
cir.getY()-sqr.getY()*1.0); //radians of the angle
double dBox; //distance from box to edge of box in direction of the circle
if((theta > Math.PI/4 && theta < 3*Math.PI / 4) ||
(theta < -Math.PI/4 && theta > -3*Math.PI / 4)) {
dBox = sqr.getS() / (2*Math.sin(theta));
} else {
dBox = sqr.getS() / (2*Math.cos(theta));
}
boolean touching = (Math.abs(dBox) >=
Math.sqrt(Math.pow(sqr.getX()-cir.getX(), 2) +
Math.pow(sqr.getY()-cir.getY(), 2)));
其他回答
有一种非常简单的方法来做到这一点,你必须在x和y上夹住一个点,但在正方形内部,当圆心在一个垂直轴上的两个正方形边界点之间时,你需要将这些坐标夹到平行轴上,只是要确保夹住的坐标不超过正方形的限制。 然后只需得到圆心与夹紧坐标之间的距离,并检查距离是否小于圆的半径。
以下是我是如何做到的(前4个点是方坐标,其余是圆点):
bool DoesCircleImpactBox(float x, float y, float x1, float y1, float xc, float yc, float radius){
float ClampedX=0;
float ClampedY=0;
if(xc>=x and xc<=x1){
ClampedX=xc;
}
if(yc>=y and yc<=y1){
ClampedY=yc;
}
radius = radius+1;
if(xc<x) ClampedX=x;
if(xc>x1) ClampedX=x1-1;
if(yc<y) ClampedY=y;
if(yc>y1) ClampedY=y1-1;
float XDif=ClampedX-xc;
XDif=XDif*XDif;
float YDif=ClampedY-yc;
YDif=YDif*YDif;
if(XDif+YDif<=radius*radius) return true;
return false;
}
有效,一周前才发现,现在才开始测试。
double theta = Math.atan2(cir.getX()-sqr.getX()*1.0,
cir.getY()-sqr.getY()*1.0); //radians of the angle
double dBox; //distance from box to edge of box in direction of the circle
if((theta > Math.PI/4 && theta < 3*Math.PI / 4) ||
(theta < -Math.PI/4 && theta > -3*Math.PI / 4)) {
dBox = sqr.getS() / (2*Math.sin(theta));
} else {
dBox = sqr.getS() / (2*Math.cos(theta));
}
boolean touching = (Math.abs(dBox) >=
Math.sqrt(Math.pow(sqr.getX()-cir.getX(), 2) +
Math.pow(sqr.getY()-cir.getY(), 2)));
def colision(rect, circle):
dx = rect.x - circle.x
dy = rect.y - circle.y
distance = (dy**2 + dx**2)**0.5
angle_to = (rect.angle + math.atan2(dx, dy)/3.1415*180.0) % 360
if((angle_to>135 and angle_to<225) or (angle_to>0 and angle_to<45) or (angle_to>315 and angle_to<360)):
if distance <= circle.rad/2.+((rect.height/2.0)*(1.+0.5*abs(math.sin(angle_to*math.pi/180.)))):
return True
else:
if distance <= circle.rad/2.+((rect.width/2.0)*(1.+0.5*abs(math.cos(angle_to*math.pi/180.)))):
return True
return False
假设你有矩形的四条边,检查从这些边到圆心的距离,如果小于半径,那么这些形状是相交的。
if sqrt((rectangleRight.x - circleCenter.x)^2 +
(rectangleBottom.y - circleCenter.y)^2) < radius
// then they intersect
if sqrt((rectangleRight.x - circleCenter.x)^2 +
(rectangleTop.y - circleCenter.y)^2) < radius
// then they intersect
if sqrt((rectangleLeft.x - circleCenter.x)^2 +
(rectangleTop.y - circleCenter.y)^2) < radius
// then they intersect
if sqrt((rectangleLeft.x - circleCenter.x)^2 +
(rectangleBottom.y - circleCenter.y)^2) < radius
// then they intersect
对于那些需要用SQL在地理坐标中计算圆/矩形碰撞的人, 这是我在oracle 11中实现的e.James建议算法。
在输入中,它需要圆坐标,圆半径km和矩形的两个顶点坐标:
CREATE OR REPLACE FUNCTION "DETECT_CIRC_RECT_COLLISION"
(
circleCenterLat IN NUMBER, -- circle Center Latitude
circleCenterLon IN NUMBER, -- circle Center Longitude
circleRadius IN NUMBER, -- circle Radius in KM
rectSWLat IN NUMBER, -- rectangle South West Latitude
rectSWLon IN NUMBER, -- rectangle South West Longitude
rectNELat IN NUMBER, -- rectangle North Est Latitude
rectNELon IN NUMBER -- rectangle North Est Longitude
)
RETURN NUMBER
AS
-- converts km to degrees (use 69 if miles)
kmToDegreeConst NUMBER := 111.045;
-- Remaining rectangle vertices
rectNWLat NUMBER;
rectNWLon NUMBER;
rectSELat NUMBER;
rectSELon NUMBER;
rectHeight NUMBER;
rectWIdth NUMBER;
circleDistanceLat NUMBER;
circleDistanceLon NUMBER;
cornerDistanceSQ NUMBER;
BEGIN
-- Initialization of remaining rectangle vertices
rectNWLat := rectNELat;
rectNWLon := rectSWLon;
rectSELat := rectSWLat;
rectSELon := rectNELon;
-- Rectangle sides length calculation
rectHeight := calc_distance(rectSWLat, rectSWLon, rectNWLat, rectNWLon);
rectWidth := calc_distance(rectSWLat, rectSWLon, rectSELat, rectSELon);
circleDistanceLat := abs( (circleCenterLat * kmToDegreeConst) - ((rectSWLat * kmToDegreeConst) + (rectHeight/2)) );
circleDistanceLon := abs( (circleCenterLon * kmToDegreeConst) - ((rectSWLon * kmToDegreeConst) + (rectWidth/2)) );
IF circleDistanceLon > ((rectWidth/2) + circleRadius) THEN
RETURN -1; -- -1 => NO Collision ; 0 => Collision Detected
END IF;
IF circleDistanceLat > ((rectHeight/2) + circleRadius) THEN
RETURN -1; -- -1 => NO Collision ; 0 => Collision Detected
END IF;
IF circleDistanceLon <= (rectWidth/2) THEN
RETURN 0; -- -1 => NO Collision ; 0 => Collision Detected
END IF;
IF circleDistanceLat <= (rectHeight/2) THEN
RETURN 0; -- -1 => NO Collision ; 0 => Collision Detected
END IF;
cornerDistanceSQ := POWER(circleDistanceLon - (rectWidth/2), 2) + POWER(circleDistanceLat - (rectHeight/2), 2);
IF cornerDistanceSQ <= POWER(circleRadius, 2) THEN
RETURN 0; -- -1 => NO Collision ; 0 => Collision Detected
ELSE
RETURN -1; -- -1 => NO Collision ; 0 => Collision Detected
END IF;
RETURN -1; -- -1 => NO Collision ; 0 => Collision Detected
END;