From 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Mon, 27 Jun 2022 17:19:28 +0200
Subject: updated tcr

---
 geometry/formulars3d.cpp | 53 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 geometry/formulars3d.cpp

(limited to 'geometry/formulars3d.cpp')

diff --git a/geometry/formulars3d.cpp b/geometry/formulars3d.cpp
new file mode 100644
index 0000000..f527d57
--- /dev/null
+++ b/geometry/formulars3d.cpp
@@ -0,0 +1,53 @@
+// Skalarprodukt
+double operator|(pt3 a, pt3 b) {
+	return a.x * b.x + a.y*b.y + a.z*b.z;
+}
+double dot(pt3 a, pt3 b) {return a|b;}
+
+// Kreuzprodukt
+pt3 operator*(pt3 a, pt3 b) {return {a.y*b.z - a.z*b.y,
+																		 a.z*b.x - a.x*b.z,
+																		 a.x*b.y - a.y*b.x};}
+pt3 cross(pt3 a, pt3 b) {return a*b;}
+
+// Länge von a
+double abs(pt3 a) {return sqrt(dot(a, a));}
+double abs(pt3 a, pt3 b) {return abs(b - a);}
+
+// Mixedprodukt
+double mixed(pt3 a, pt3 b, pt3 c) {return a*b|c;};
+
+// orientierung von p zu der Ebene durch a, b, c
+// -1 => gegen den Uhrzeigersinn,
+//  0 => kolliniear,
+//  1 => im Uhrzeigersinn.
+int orientation(pt3 a, pt3 b, pt3 c, pt3 p) {
+	double orien = mixed(b - a, c - a, p - a);
+	return (orien > EPS) - (orien < -EPS);
+}
+
+// Entfernung von Punkt p zur Ebene a,b,c.
+double distToPlane(pt3 a, pt3 b, pt3 c, pt3 p) {
+	pt3 n = cross(b-a, c-a);
+	return (abs(dot(n, p)) - dot(n, a)) / abs(n);
+}
+
+// Liegt p in der Ebene a,b,c?
+bool pointOnPlane(pt3 a, pt3 b, pt3 c, pt3 p) {
+	return orientation(a, b, c, p) == 0;
+}
+
+// Schnittpunkt von der Grade a-b und der Ebene c,d,e
+// die Grade darf nicht parallel zu der Ebene sein!
+pt3 linePlaneIntersection(pt3 a, pt3 b, pt3 c, pt3 d, pt3 e) {
+	pt3 n = cross(d-c, e-c);
+	pt3 d = b - a;
+	return a - d * (dot(n, a) - dot(n, c)) / dot(n, d);
+}
+
+// Abstand zwischen der Grade a-b und c-d
+double lineLineDist(pt3 a, pt3 b, pt3 c, pt3 d) {
+	pt3 n = cross(b - a, d - c);
+	if (abs(n) < EPS) return distToLine(a, b, c);
+	return abs(dot(a - c, n)) / abs(n);
+}
\ No newline at end of file
-- 
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