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========================================================
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Projekt: gamematrix (C++ Library)
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Rolle: Architekt
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Datei: design.txt
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Datum: 03.11.2025
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Team: prog3b_652
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========================================================
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# ----------------------------
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# 1. Projektstruktur / Namespace
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# ----------------------------
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Namespace: Matrix3D
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Ziel: Saubere Trennung der Bibliothek, Vermeidung von Namenskonflikten.
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Beispiel:
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namespace Matrix3D {
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// Funktionen, ggf Klasse(n)
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}
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# ----------------------------
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# 2. Datenstrukturen / Klassen
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# ----------------------------
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Listen Sie die Klassen oder Structs auf, die verwendet werden:
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| Name | Typ | Beschreibung |
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|--------|------------------------------------------|----------------------|
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| Vec3 | struct Vec3 | 3D-Vektor (x, y, z) |
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| Mat4 | std::array<std::array<double,4>,4> | 4x4-Matrix (homogen) |
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| Vec4 | struct Vec4 | 4D-Vektor (x, y, z, w|
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| Vec2 | struct Vec2 | 2D-Vektor (x, y) |
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# ----------------------------
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# 3. Operatoren / Templates
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# ----------------------------
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Welche Operatoren oder Templates sollen definiert werden?
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- Templates für unterschiedliche Datentypen? - Ja
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- Operatoren:
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- Mat4 * Mat4
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- Mat4 * Vec3
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# ----------------------------
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# 4. Funktionen / Schnittstellen
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# ----------------------------
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Liste der Funktionen mit Eingabe/Ausgabe und kurzer Beschreibung:
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| Funktion | Eingabe | Ausgabe | Kurzbeschreibung |
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|---------------|------------------------------------|-----------------------|----------------------------------------|
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| matmul | Mat4 A, Mat4 B | Mat4 | Matrixmultiplikation 4x4 |
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| translate | Vec3 pos | Mat4 | Verschiebungstransformation |
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| rot3D | double angle_deg, char axis | Mat4 | Rotation um Achse x/y/z |
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| identity (optional)| --- | Mat4 | Identitätsmatrix |
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| _____________ | __________________________________ | ____________________ | ______________________________ |
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# ----------------------------
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# 5. Designentscheidungen / Hinweise
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# ----------------------------
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- Rückgabe der Matrizen per Wert oder Referenz? per Wert
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- Verwendung von std::array oder std::vector? std::array
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- Homogene Koordinaten für Translation / Rotation (4x4)? - Ja
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- Weitere Designüberlegungen: Nutzung von Templates für float/double
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# ----------------------------
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# 6. Deliverables / Milestones
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# ----------------------------
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- design.txt fertig und im Branch architect committed
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- Übergabe an Entwickler für Implementierung
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========================================================
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Hinweis:
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- Dieses Dokument dient als Grundlage für die Implementierung.
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- Alle Designentscheidungen sollen klar nachvollziehbar sein.
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========================================================
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@@ -1,44 +0,0 @@
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@@ -1,43 +0,0 @@
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========================================================
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Projekt: gamematrix (C++ Library)
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Rolle: Tester
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Datei: tests.txt
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Datum: 4.10.2025
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Team: prog3b_652
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========================================================
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# ----------------------------
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# 1. Testplan Übersicht
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# ----------------------------
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Ziel: Überprüfung der Funktionen matmul(), translate(), rot3D().
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| Funktion | Testfall | Eingabe | Erwartetes Ergebnis | Bemerkung |
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|---------------|---------------------------|------------------------------|-----------------------------------|----------------------------|
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| matmul | Identity * Identity | 4x4 Identity Matrizen | Identity | Basisfall |
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| matmul | Beispielmatrizen | A=[[...]], B=[[...]] | C=[[...]] | Prüfen mit Handrechnung |
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| translate | Verschiebung | Vec3 {1,2,3} | Matrix mit Translation 1,2,3 | Prüfen letzte Spalte |
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| rot3D | Rotation Z 90° | angle_deg=90, axis='z' | (1,0,0) -> (0,1,0) | Prüfen Anwendung auf Vektor|
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| rot3D | Rotation X 180° | angle_deg=180, axis='x' | (0,1,0) -> (0,-1,0) | Prüfen Anwendung auf Vektor|
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| rot3D | Rotation Y 270° | angle_deg=270, axis='y' | (1,0,0) -> (0,0,-1) | Prüfen Anwendung auf Vektor|
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# ----------------------------
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# 2. Testdaten / Matrizen
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# ----------------------------
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- Matrizen für matmul: Identity, Beispiel A/B Matrizen
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- Vektoren für translate: Vec3 {x, y, z}
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- Vektoren für rot3D: Vec3 {1,0,0}, Vec3 {0,1,0}
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# ----------------------------
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# 3. Abnahmekriterien
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# ----------------------------
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- Alle Unit-Tests erfolgreich
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- Keine Exceptions außer gewollt (z. B. ungültige Achse)
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- Testbericht in tests.txt dokumentiert
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========================================================
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Hinweis:
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- Diese Datei wird vom Tester gepflegt.
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- Tester dokumentiert Input, Output, erwartetes Ergebnis und Erfolg/Fehler.
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========================================================
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//
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// Created by kris- on 03.11.2025.
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//
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#include <iostream>
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#include "gamematrix.h"
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// Matrixmultiplikation
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// Rotationsmatrix um Achse x/y/z
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static std::array<std::array<double,4>,4> rot3D(double angle_deg, char axis);
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// Verschiebung
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static std::array<std::array<double,4>,4> translate(const std::array<double, 3>& pos);
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//Matrixmultiplikation-Funktion
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std::array<std::array<double,4>,4> gameMatrix::matmul(
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const std::array<std::array<double,4>,4>& A,
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const std::array<std::array<double,4>,4>& B)
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{ //Matrix-Mathematik (Matrix C = A*B)
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std::array<std::array<double,4>,4> C{};
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for (int i = 0; i < 4; ++i)
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for (int j = 0; j < 4; ++j)
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for (int k = 0; k < 4; ++k)
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C[i][j] += A[i][k] * B[k][j];
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return C;
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}
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//Rotation 3D
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std::array<std::array<double,4>,4> gameMatrix::rot3D(double angle_deg, char axis) {
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double rad = angle_deg * M_PI / 180.0;
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//Mathematik-Rotation
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std::array<std::array<double,4>,4> R{};
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for (int i = 0; i < 4; ++i)
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R[i][i] = 1.0;
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if (axis == 'x' || axis == 'X') {
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R[1][1] = cos(rad);
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R[1][2] = -sin(rad);
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R[2][1] = sin(rad);
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R[2][2] = cos(rad);
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} else if (axis == 'y' || axis == 'Y') {
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R[0][0] = cos(rad);
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R[0][2] = sin(rad);
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R[2][0] = -sin(rad);
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R[2][2] = cos(rad);
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} else if (axis == 'z' || axis == 'Z') {
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R[0][0] = cos(rad);
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R[0][1] = -sin(rad);
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R[1][0] = sin(rad);
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R[1][1] = cos(rad);
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}
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return R;
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}
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//Translation
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std::array<std::array<double,4>,4> gameMatrix::translate(const std::array<double,3>& pos) {
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std::array<std::array<double,4>,4> T{};
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for (int i = 0; i < 4; ++i)
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T[i][i] = 1.0; // Identitätsmatrix
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T[0][3] = pos[0]; // x-Verschiebung
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T[1][3] = pos[1]; // y-Verschiebung
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T[2][3] = pos[2]; // z-Verschiebung
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return T;
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}
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int main()
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{
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// Part Matrix
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std::array<std::array<double,4>,4> A{};
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std::array<std::array<double,4>,4> B{};
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std::cout << "Gib die Werte für Matrix A (4x4) ein:\n";
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for (int i = 0; i < 4; ++i)
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for (int j = 0; j < 4; ++j) {
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std::cout << "A[" << i << "][" << j << "] = ";
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std::cin >> A[i][j];
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}
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std::cout << "\nGib die Werte für Matrix B (4x4) ein:\n";
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for (int i = 0; i < 4; ++i)
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for (int j = 0; j < 4; ++j) {
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std::cout << "B[" << i << "][" << j << "] = ";
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std::cin >> B[i][j];
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}
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std::array<std::array<double,4>,4> C = gameMatrix::matmul(A, B);
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std::cout << "\nErgebnis der Matrixmultiplikation (C = A * B):\n";
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for (int i = 0; i < 4; ++i) {
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for (int j = 0; j < 4; ++j)
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std::cout << C[i][j] << "\t";
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std::cout << "\n";
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}
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//Ende Matrix
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// Rotation
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double angle;
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char axis;
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std::cout << "\nGib einen Rotationswinkel in Grad ein: ";
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std::cin >> angle;
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std::cout << "Gib die Rotationsachse (x/y/z) ein: ";
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std::cin >> axis;
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std::array<std::array<double,4>,4> R = gameMatrix::rot3D(angle, axis);
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std::cout << "\nRotationsmatrix R:\n";
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for (int i = 0; i < 4; ++i) {
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for (int j = 0; j < 4; ++j)
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std::cout << R[i][j] << "\t";
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std::cout << "\n";
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}
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// Translation
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std::array<double,3> pos;
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std::cout << "\nGib die Translation (x y z) ein: ";
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std::cin >> pos[0] >> pos[1] >> pos[2];
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std::array<std::array<double,4>,4> T = gameMatrix::translate(pos);
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std::cout << "\nTranslationsmatrix T:\n";
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for (int i = 0; i < 4; ++i) {
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for (int j = 0; j < 4; ++j)
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std::cout << T[i][j] << "\t";
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std::cout << "\n";
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}
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return 0;
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}
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@@ -1,19 +0,0 @@
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#pragma once
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#include <vector>
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#include <array>
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#include <stdexcept>
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#include <cmath>
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class gameMatrix
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{
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public:
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// Matrix Multiplikation
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static std::array<std::array<double,4>,4> matmul(const std::array<std::array<double,4>,4>& A,
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const std::array<std::array<double,4>,4>& B);
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// Rotationsmatrix um Achse x/y/z
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static std::array<std::array<double,4>,4> rot3D(double angle_deg, char axis);
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// Verschiebung
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static std::array<std::array<double,4>,4> translate(const std::array<double, 3>& pos);
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};
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@@ -1,41 +0,0 @@
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#include <iostream>
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#include <array>
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#include <cassert>
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#include <cmath>
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#include "gamematrix.h"
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// Matrix-Vektor Multiplikation (4x4 Matrix auf 4D Vektor anwenden)
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std::array<double, 4> matVecMul(const std::array<std::array<double, 4>, 4>& mat, const std::array<double, 4>& vec) {
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std::array<double, 4> result = {0, 0, 0, 0};
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for (size_t i = 0; i < 4; ++i) {
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for (size_t j = 0; j < 4; ++j) {
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result[i] += mat[i][j] * vec[j];
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}
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}
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return result;
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}
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void test_rotateZ() {
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std::array<double, 4> v = {1, 0, 0, 1}; // Der Vektor (1, 0, 0) wird zu (1, 0, 0, 1)
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// Rotationsmatrix um 90° um die Z-Achse
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auto R = gameMatrix::rot3D(90, 'Z');
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// Vektor mit der Matrix multiplizieren
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std::array<double, 4> result = matVecMul(R, v);
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// Erwartetes Ergebnis
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std::array<double, 4> expected_result = {0, 1, 0, 1};
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// Vergleich der Ergebnisse
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for (size_t i = 0; i < 4; ++i) {
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assert(std::abs(result[i] - expected_result[i]) < 1e-6);
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}
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std::cout << "Test erfolgreich! Rotation um Z-Achse funktioniert." << std::endl;
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}
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int main() {
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test_rotateZ();
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return 0;
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}
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