Math 如何检查两个旋转矩形之间的交点？
有人能解释一下如何检查一个旋转的矩形是否与另一个矩形相交吗Math 如何检查两个旋转矩形之间的交点？,math,intersection,rect,Math,Intersection,Rect,有人能解释一下如何检查一个旋转的矩形是否与另一个矩形相交吗 对于两个多边形中的每条边，请检查它是否可以用作分隔线。如果是这样，您就完成了：无交叉口 如果未找到分隔线，则有一个交点 ///检查两个多边形是否相交。 布尔多边形相交（多边形a、多边形b） { foreach（新[]{a，b}中的var多边形） { 对于（int i1=0；i1
///检查两个多边形是否相交。
布尔多边形相交（多边形a、多边形b）
{
foreach（新[]{a，b}中的var多边形）
{
对于（int i1=0；i1maxA）
maxA=预测值；
}
double？minB=null，maxB=null；
foreach（b点中的var p）
{
预计风险值=正常.X*p.X+正常.Y*p.Y；
if（minB==null | |投影maxB）
maxB=预测值；
}
if（maxA NB:该算法仅适用于按顺时针或逆时针顺序指定的凸多边形。在javascript中，完全相同的算法是（为方便起见）：
/**
*用于确定所述两个多边形之间是否存在交点的辅助函数
*通过顶点列表。使用分离轴定理
*
*@param一组连接点[{x:，y:}，{x:，y:}，…]构成一个闭合多边形
*@param b一组连接点[{x:，y:}，{x:，y:}，…]构成一个闭合多边形
*@如果两个多边形之间存在任何交点，则返回true，否则返回false
*/
函数doPolygonsIntersect（a，b）{
var多边形=[a，b]；
var minA，maxA，projected，i，i1，j，minB，maxB；
对于（i=0；i最大值）{
maxA=预测值；
}
}
//对于第二个形状中的每个顶点，将其投影到与边垂直的线上
//并跟踪这些值的最小值和最大值
minB=maxB=未定义；
对于（j=0；j最大值）{
maxB=预测值；
}
}
//如果两个项目之间没有重叠，那么我们所看到的边缘将两者分开
//多边形，我们知道没有重叠
if（maxA 希望这对别人有帮助 查看Oren Becker设计的检测旋转矩形与形状相交的方法：
struct _Vector2D
{
float x, y;
};
// C:center; S: size (w,h); ang: in radians,
// rotate the plane by [-ang] to make the second rectangle axis in C aligned (vertical)
struct _RotRect
{
_Vector2D C;
_Vector2D S;
float ang;
};
// Rotated Rectangles Collision Detection, Oren Becker, 2001
bool check_two_rotated_rects_intersect(_RotRect * rr1, _RotRect * rr2)
{
_Vector2D A, B, // vertices of the rotated rr2
C, // center of rr2
BL, TR; // vertices of rr2 (bottom-left, top-right)
float ang = rr1->ang - rr2->ang, // orientation of rotated rr1
cosa = cos(ang), // precalculated trigonometic -
sina = sin(ang); // - values for repeated use
float t, x, a; // temporary variables for various uses
float dx; // deltaX for linear equations
float ext1, ext2; // min/max vertical values
// move rr2 to make rr1 cannonic
C = rr2->C;
SubVectors2D(&C, &rr1->C);
// rotate rr2 clockwise by rr2->ang to make rr2 axis-aligned
RotateVector2DClockwise(&C, rr2->ang);
// calculate vertices of (moved and axis-aligned := 'ma') rr2
BL = TR = C;
/*SubVectors2D(&BL, &rr2->S);
AddVectors2D(&TR, &rr2->S);*/
//-----------------------------------
BL.x -= rr2->S.x/2; BL.y -= rr2->S.y/2;
TR.x += rr2->S.x/2; TR.y += rr2->S.y/2;
// calculate vertices of (rotated := 'r') rr1
A.x = -(rr1->S.y/2)*sina; B.x = A.x; t = (rr1->S.x/2)*cosa; A.x += t; B.x -= t;
A.y = (rr1->S.y/2)*cosa; B.y = A.y; t = (rr1->S.x/2)*sina; A.y += t; B.y -= t;
//---------------------------------------
//// calculate vertices of (rotated := 'r') rr1
//A.x = -rr1->S.y*sina; B.x = A.x; t = rr1->S.x*cosa; A.x += t; B.x -= t;
//A.y = rr1->S.y*cosa; B.y = A.y; t = rr1->S.x*sina; A.y += t; B.y -= t;
t = sina*cosa;
// verify that A is vertical min/max, B is horizontal min/max
if (t < 0)
{
t = A.x; A.x = B.x; B.x = t;
t = A.y; A.y = B.y; B.y = t;
}
// verify that B is horizontal minimum (leftest-vertex)
if (sina < 0) { B.x = -B.x; B.y = -B.y; }
// if rr2(ma) isn't in the horizontal range of
// colliding with rr1(r), collision is impossible
if (B.x > TR.x || B.x > -BL.x) return 0;
// if rr1(r) is axis-aligned, vertical min/max are easy to get
if (t == 0) {ext1 = A.y; ext2 = -ext1; }
// else, find vertical min/max in the range [BL.x, TR.x]
else
{
x = BL.x-A.x; a = TR.x-A.x;
ext1 = A.y;
// if the first vertical min/max isn't in (BL.x, TR.x), then
// find the vertical min/max on BL.x or on TR.x
if (a*x > 0)
{
dx = A.x;
if (x < 0) { dx -= B.x; ext1 -= B.y; x = a; }
else { dx += B.x; ext1 += B.y; }
ext1 *= x; ext1 /= dx; ext1 += A.y;
}
x = BL.x+A.x; a = TR.x+A.x;
ext2 = -A.y;
// if the second vertical min/max isn't in (BL.x, TR.x), then
// find the local vertical min/max on BL.x or on TR.x
if (a*x > 0)
{
dx = -A.x;
if (x < 0) { dx -= B.x; ext2 -= B.y; x = a; }
else { dx += B.x; ext2 += B.y; }
ext2 *= x; ext2 /= dx; ext2 -= A.y;
}
}
// check whether rr2(ma) is in the vertical range of colliding with rr1(r)
// (for the horizontal range of rr2)
return !((ext1 < BL.y && ext2 < BL.y) ||
(ext1 > TR.y && ext2 > TR.y));
}
inline void AddVectors2D(_Vector2D * v1, _Vector2D * v2)
{
v1->x += v2->x; v1->y += v2->y;
}
inline void SubVectors2D(_Vector2D * v1, _Vector2D * v2)
{
v1->x -= v2->x; v1->y -= v2->y;
}
inline void RotateVector2DClockwise(_Vector2D * v, float ang)
{
float t, cosa = cos(ang), sina = sin(ang);
t = v->x;
v->x = t*cosa + v->y*sina;
v->y = -t*sina + v->y*cosa;
}
bool IsIntersecting(UIElement element1, UIElement element2)
{
Rect area1 = new Rect(
(double)element1.GetValue(Canvas.TopProperty),
(double)element1.GetValue(Canvas.LeftProperty),
(double)element1.GetValue(Canvas.WidthProperty),
(double)element1.GetValue(Canvas.HeightProperty));
Rect area2 = new Rect(
(double)element2.GetValue(Canvas.TopProperty),
(double)element2.GetValue(Canvas.LeftProperty),
(double)element2.GetValue(Canvas.WidthProperty),
(double)element2.GetValue(Canvas.HeightProperty));
Transform transform1 = element1.RenderTransform as Transform;
Transform transform2 = element2.RenderTransform as Transform;
if (transform1 != null)
{
area1.Transform(transform1.Value);
}
if (transform2 != null)
{
area2.Transform(transform2.Value);
}
return area1.IntersectsWith(area2);
}
math.inf = 1e309
function love.load()
pol = {{0, 0}, {30, 2}, {8, 30}}
pol2 = {{60, 60}, {90, 61}, {98, 100}, {80, 100}}
end
function love.draw()
for k,v in ipairs(pol) do
love.graphics.line(pol[k][1], pol[k][2], pol[k % #pol + 1][1], pol[k % #pol + 1][2])
end
for k,v in ipairs(pol2) do
love.graphics.line(pol2[k][1], pol2[k][2], pol2[k % #pol2 + 1][1], pol2[k % #pol2 + 1][2])
end
end
function love.update(dt)
pol[1][1] = love.mouse.getX()
pol[1][2] = love.mouse.getY()
pol[2][1] = pol[1][1] + 30
pol[2][2] = pol[1][2] + 2
pol[3][1] = pol[1][1] + 8
pol[3][2] = pol[1][2] + 30
--lazy way to see that's function works
print(doPolygonsIntersect(pol, pol2))
end
-------------------------------------------------------------------------
function doPolygonsIntersect(a,b)
polygons = {a,b}
for i=1, #polygons do
polygon = polygons[i]
for i1=1, #polygon do
i2 = i1 % #polygon + 1
p1 = polygon[i1]
p2 = polygon[i2]
nx,ny = p2[2] - p1[2], p1[1] - p2[1]
minA = math.inf
maxA = -math.inf
for j=1, #a do
projected = nx * a[j][1] + ny * a[j][2]
if projected < minA then minA = projected end
if projected > maxA then maxA = projected end
end
minB = math.inf
maxB = -math.inf
for j=1, #b do
projected = nx * b[j][1] + ny * b[j][2]
if projected < minB then minB = projected end
if projected > maxB then maxB = projected end
end
if maxA < minB or maxB < minA then return false end
end
end
return true
end
def do_polygons_intersect(a, b):
"""
* Helper function to determine whether there is an intersection between the two polygons described
* by the lists of vertices. Uses the Separating Axis Theorem
*
* @param a an ndarray of connected points [[x_1, y_1], [x_2, y_2],...] that form a closed polygon
* @param b an ndarray of connected points [[x_1, y_1], [x_2, y_2],...] that form a closed polygon
* @return true if there is any intersection between the 2 polygons, false otherwise
"""
polygons = [a, b];
minA, maxA, projected, i, i1, j, minB, maxB = None, None, None, None, None, None, None, None
for i in range(len(polygons)):
# for each polygon, look at each edge of the polygon, and determine if it separates
# the two shapes
polygon = polygons[i];
for i1 in range(len(polygon)):
# grab 2 vertices to create an edge
i2 = (i1 + 1) % len(polygon);
p1 = polygon[i1];
p2 = polygon[i2];
# find the line perpendicular to this edge
normal = { 'x': p2[1] - p1[1], 'y': p1[0] - p2[0] };
minA, maxA = None, None
# for each vertex in the first shape, project it onto the line perpendicular to the edge
# and keep track of the min and max of these values
for j in range(len(a)):
projected = normal['x'] * a[j][0] + normal['y'] * a[j][1];
if (minA is None) or (projected < minA):
minA = projected
if (maxA is None) or (projected > maxA):
maxA = projected
# for each vertex in the second shape, project it onto the line perpendicular to the edge
# and keep track of the min and max of these values
minB, maxB = None, None
for j in range(len(b)):
projected = normal['x'] * b[j][0] + normal['y'] * b[j][1]
if (minB is None) or (projected < minB):
minB = projected
if (maxB is None) or (projected > maxB):
maxB = projected
# if there is no overlap between the projects, the edge we are looking at separates the two
# polygons, and we know there is no overlap
if (maxA < minB) or (maxB < minA):
print("polygons don't intersect!")
return False;
return True
/// Checks if the two Phaser 3 polygons are intersecting.
gameScene.doPolygonsIntersect=function(a, b) {
// https://stackoverflow.com/questions/10962379/how-to-check-intersection-between-2-rotated-rectangles#10965077
/**
* Helper function to determine whether there is an intersection between the two polygons described
* by the lists of vertices. Uses the Separating Axis Theorem
*
* @param a an array of connected points [{x:, y:}, {x:, y:},...] that form a closed polygon
* @param b an array of connected points [{x:, y:}, {x:, y:},...] that form a closed polygon
* @return true if there is any intersection between the 2 polygons, false otherwise
*/
var polygons = [a, b];
var minA, maxA, projected, i, i1, j, minB, maxB;
for (i = 0; i < polygons.length; i++) {
// for each polygon, look at each edge of the polygon, and determine if it separates
// the two shapes
var polygon = polygons[i];
for (i1 = 0; i1 < polygon.points.length; i1++) {
// grab 2 vertices to create an edge
var i2 = (i1 + 1) % polygon.points.length;
var p1 = polygon.points[i1];
var p2 = polygon.points[i2];
// find the line perpendicular to this edge
var normal = { x: p2.y - p1.y, y: p1.x - p2.x };
minA = maxA = undefined;
// for each vertex in the first shape, project it onto the line perpendicular to the edge
// and keep track of the min and max of these values
for (j = 0; j < a.points.length; j++) {
projected = normal.x * a.points[j].x + normal.y * a.points[j].y;
if (!isDef(minA) || projected < minA) {
minA = projected;
}
if (!isDef(maxA) || projected > maxA) {
maxA = projected;
}
}
// for each vertex in the second shape, project it onto the line perpendicular to the edge
// and keep track of the min and max of these values
minB = maxB = undefined;
for (j = 0; j < b.points.length; j++) {
projected = normal.x * b.points[j].x + normal.y * b.points[j].y;
if (!isDef(minB) || projected < minB) {
minB = projected;
}
if (!isDef(maxB) || projected > maxB) {
maxB = projected;
}
}
// if there is no overlap between the projects, the edge we are looking at separates the two
// polygons, and we know there is no overlap
if (maxA < minB || maxB < minA) {
console.log("polygons don't intersect!");
return false;
}
}
}
return true;
};
function doPolygonsIntersect(a, b)
local polygons = { a, b };
local minA, maxA, projected, i, i1, j, minB, maxB;
for i = 1, #polygons do
--// for each polygon, look at each edge of the polygon, and determine if it separates
--// the two shapes
local polygon = polygons[i];
for i1 = 0, (#polygon-1) do
--// grab 2 vertices to create an edge
local i2 = (i1 + 1) % (#polygon);
local p1 = polygon[i1+1];
local p2 = polygon[i2+1];
--// find the line perpendicular to this edge
local normal = { x = p2.y - p1.y, y = p1.x - p2.x };
minA = nil;
maxA = nil;
--// for each vertex in the first shape, project it onto the line perpendicular to the edge
--// and keep track of the min and max of these values
for j = 1, #a do
projected = normal.x * a[j].x + normal.y * a[j].y;
if (minA == nil or projected < minA) then
minA = projected;
end
if (maxA == nil or projected > maxA) then
maxA = projected;
end
end
--// for each vertex in the second shape, project it onto the line perpendicular to the edge
--// and keep track of the min and max of these values
minB = nil;
maxB = nil;
for j = 1, #b do
projected = normal.x * b[j].x + normal.y * b[j].y;
if (minB == nil or projected < minB) then
minB = projected;
end
if (maxB == nil or projected > maxB) then
maxB = projected;
end
end
if (maxA < minB or maxB < minA) then
return false;
end
end
end
return true;
end