)
Ja, wenn man das so aufgezeichnet bekommt, dann wird es einfacher. Und vor allem: Ich bin auf ein xy Problem gelaufen:
public static boolean pointInOrientedRectangle(
float halfX, float halfY, // <- halbe Seitenlängen des Rechtecks
float centerX, float centerY, // <- Zentrum des Rechtecks
float angle, // <- Rotationswinkel (im mathematischen Sinne: positive Werte rotieren gegen den Uhrzeigersinn)
// Rotation erfolgt um das Zentrum des Rechtecks
float px, float py) { // <- zu testender Punkt
// Translation und Rotation als 3x2 matrix
float cos = (float) Math.cos(angle), sin = (float) Math.sin(angle);
float m10 = -sin * halfY, m11 = cos * halfY;
float m00 = cos * halfX, m01 = sin * halfX;
float m20 = centerX, m21 = centerY;
// 3x2 matrix invertieren
float s = 1.0f / (m00 * m11 - m01 * m10);
float n00 = m11 * s, n01 = -m01 * s;
float n10 = -m10 * s, n11 = m00 * s;
float n20 = (m10 * m21 - m20 * m11) * s, n21 = (m20 * m01 - m00 * m21) * s;
// M * (px, py, 1)
float dpx = n00 * px + n10 * py + n20;
float dpy = n01 * px + n11 * py + n21;
return dpx >= -1.0f && dpy >= -1.0f && dpx <= 1.0f && dpy <= 1.0f;
}public static boolean pointInOrientedRectangle(
float halfX, float halfY,
float centerX, float centerY,
float angle,
float px, float py) {
float cos = (float) Math.cos(-angle), sin = (float) Math.sin(-angle);
float n00 = cos / halfX, n01 = sin / halfY;
float n10 = -sin / halfX, n11 = cos / halfY;
float dpx = n00 * px + n10 * py + n00 * -centerX + n10 * -centerY;
float dpy = n01 * px + n11 * py + n01 * -centerX + n11 * -centerY;
return dpx >= -1.0f && dpy >= -1.0f && dpx <= 1.0f && dpy <= 1.0f;
}
import sys
import numpy as np
from PyQt5.QtGui import QPainter, QColor
from PyQt5.QtWidgets import QWidget, QApplication
points = [np.array((400, 400)), np.array((100, 450)), np.array((100, 600)), np.array((400, 550))]
sides = [points[(i + 1) % 4] - points[i] for i in range(4)]
normals = [np.array([p[1], -p[0]]) for p in sides]
tested = []
def test(p, v, t):
return (t - p).dot(v) > 0
class Example(QWidget):
def __init__(self):
super().__init__()
self.setGeometry(300, 300, 800, 800)
self.setWindowTitle('RectangleTest')
self.show()
def paintEvent(self, event):
qp = QPainter()
qp.begin(self)
for i in range(4):
qp.drawLine(*points[i - 1], *points[i])
for p, c in tested:
qp.setBrush(QColor(*c))
s = np.array([10, 10])
qp.drawEllipse(*(p - s / 2), *s)
qp.setBrush(QColor(0, 0, 0))
qp.end()
def mousePressEvent(self, event):
pos = np.array([event.pos().x(), event.pos().y()])
res = [test(p, n, pos) for p, n in zip(points, normals)]
print(res, all(res))
tested.append((pos, (0, 255, 0) if all(res) else (255, 0, 0)))
self.repaint()
if __name__ == '__main__':
app = QApplication([])
ex = Example()
sys.exit(app.exec_())
| px py 1 |
| qx qy 1 | = (rx - px)(ry + py) + (qx - rx)(ry + ry) + (px - qx)(py + qy) =: f(p,q,r) = A
| rx ry 1 |
