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| -rw-r--r-- | geometry/formulars.cpp | 27 | ||||
| -rw-r--r-- | tcr.pdf | bin | 313603 -> 315778 bytes |
2 files changed, 26 insertions, 1 deletions
diff --git a/geometry/formulars.cpp b/geometry/formulars.cpp index 6984be9..5369b50 100644 --- a/geometry/formulars.cpp +++ b/geometry/formulars.cpp @@ -55,4 +55,29 @@ bool pointOnLine(pt a, pt b, pt p) { //testet, ob d in der gleichen Ebene liegt wie a, b, und c bool isCoplanar(pt a, pt b, pt c, pt d) { return (b - a) * (c - a) * (d - a) == 0; -}
\ No newline at end of file +} +//berechnet den Flaecheninhalt eines Polygons (nicht selbstschneidend) +double areaOfPolygon(vector<pt> &polygon) { //jeder Eckpunkt nur einmal im Vektor + double res = 0; int n = polygon.size(); + for (int i = 0; i < (int)polygon.size(); i++) + res += real(polygon[i]) * imag(polygon[(i + 1) % n]) - real(polygon[(i + 1) % n]) * imag(polygon[i]); + return 0.5 * abs(res); +} +//testet, ob sich zwei Rechtecke (p1, p2) und (p3, p4) schneiden (jeweils gegenueberliegende Ecken) +bool rectIntersection(pt p1, pt p2, pt p3, pt p4) { + double minx12 = min(real(p1), real(p2)), maxx12 = max(real(p1), real(p2)); + double minx34 = min(real(p3), real(p4)), maxx34 = max(real(p3), real(p4)); + double miny12 = min(imag(p1), imag(p2)), maxy12 = max(imag(p1), imag(p2)); + double miny34 = min(imag(p3), imag(p4)), maxy34 = max(imag(p3), imag(p4)); + return (maxx12 >= minx34) && (maxx34 >= minx12) && (maxy12 >= miny34) && (maxy34 >= miny12); +} +//testet, ob ein Punkt im Polygon liegt (beliebige Polygone) +bool pointInPolygon(pt p, vector<pt> &polygon) { //jeder Eckpunkt nur einmal im Vektor + pt rayEnd = p + pt(1, 1000000); + int counter = 0, n = polygon.size(); + for (int i = 0; i < n; i++) { + pt start = polygon[i], end = polygon[(i + 1) % n]; + if (lineSegmentIntersection(p, rayEnd, start, end)) counter++; + } + return counter & 1; +} Binary files differ |