So basically I need to do it in this order:

1.) Translate the triangle so that it's at the origin.

2.) Rotate the triangle.

3.) Translate the triangle so that it's back at it's original location.

Now, from what I understand, I need to use a Combo Matrix. Basically combine 3 matrices into 1. Now what I don't know is if I need to write this combo matrix from scratch, or I need to just simply multiply the matrices within the code. Any tips or help would be greatly appreciated! Thanks in advance!

.cpp file:

/* composition.cpp simple animation using a composition transformation matrix */ #include <stdio.h> #include <windows.h> #include "resource.h" // your path for this include may vary #include "GraphicsFramework.h" #include "gmath.h" // Global variable to store the graphics framwork object GraphicsFramework* PGraphics; HWND HOutput = 0; // handle to the output control HWND HDialog = 0; // function to draw a line between two points void DrawLine(int x1, int y1, int x2, int y2, unsigned int color) { int dx, dy; // dy / dx is the slope int x, y; // loop and point variables // calculate changes in y and x between the points dy = y2 - y1; dx = x2 - x1; if (Abs(dy) > Abs(dx)) { // since there is a greater change in y than x we must // loop in y, calculate x and draw for (y=y1; y != y2; y += Sign(dy)) { x = x1 + (y - y1) * dx / dy; PGraphics->AddPoint(x, y, color); } } else { // since there is a greater (or equal) change in x than y we must // loop in x, calculate y and draw for (x=x1; x != x2; x += Sign(dx)) { y = y1 + (x - x1) * dy / dx; PGraphics->AddPoint(x, y, color); } } // draw the last pixel PGraphics->AddPoint(x2, y2, color); } void DrawStuff() { COLORREF green = RGB(0, 255, 0); // green color to draw with COLORREF red = RGB(0, 0, 255); // red color to draw with char str[32]; // string to store user input Vector3 pts[3]; // original data points Vector3 newPts[3]; // transformed points double angle; // rotation angle Matrix4 rz; // current rotation matrix about z axis // this composite matrix need to remember its value between calls to this draw function // so it must be declared static or made a global variable static Matrix4 c; // composition matrix // set up the original points for the triangle pts[0].set( 0, 0, 0); pts[1].set(100, 100, 0); pts[2].set(100, 0, 0); // clear the scene and add an axis PGraphics->ClearScene(RGB(0, 0, 0)); PGraphics->AddAxis(RGB(150, 150, 150), 10); // get the user input from the edit boxes and // convert string input to double GetDlgItemText(HDialog, IDC_EDIT_ANGLE, str, 32); angle = atof(str); // make the current rotation matrix rz.makeRotationMatrixZ(angle); // update the composite matrix - remember we must pre-multiply by m: c = m x c c = Multiply(rz, c); // transform the original triangle points into the new points for drawing for (int i=0; i < 3; i++) { newPts[i] = Multiply(c, pts[i]); } // draw the triangle lines 0-1, 1-2, 2-0 DrawLine(newPts[0].x, newPts[0].y, newPts[1].x, newPts[1].y, green); DrawLine(newPts[1].x, newPts[1].y, newPts[2].x, newPts[2].y, green); DrawLine(newPts[2].x, newPts[2].y, newPts[0].x, newPts[0].y, green); // draw the points PGraphics->Draw(); } /* DialogProc this is the window event handler for the main dialog */ BOOL CALLBACK DialogProc (HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam) { switch(message) { case WM_INITDIALOG: // dialog is initializing - store the picture box handle in a global variable for later HOutput = GetDlgItem(hwnd, IDC_PICTURE_OUTPUT); // instantiate and initialize our graphics framework object PGraphics = new GraphicsFramework(HOutput); break; case WM_COMMAND: switch(LOWORD(wParam)) { case IDC_BTN_DRAW: // draw button was pressed DrawStuff(); break; case IDC_BTN_CLEAR: // clear button was pressed so clear the scene and draw the empty scene PGraphics->ClearScene(RGB(0, 0, 0)); PGraphics->Draw(); break; case IDCANCEL: // user is quitting so release the GraphicsFramework object and quit delete PGraphics; PostQuitMessage(0); break; } } return FALSE; } // this is the main function that starts the application int WINAPI WinMain(HINSTANCE hInst, HINSTANCE hPrevInst, char * cmdParam, int cmdShow) { // create the main window // store its handle in a global if needed HDialog = CreateDialog (GetModuleHandle(NULL), MAKEINTRESOURCE(IDD_DIALOG1), 0, DialogProc); // make the dialog visible ShowWindow(HDialog, SW_SHOW); // standard windows message loop MSG msg; int status; while ((status = GetMessage (&msg, 0, 0, 0)) != 0) { if (status == -1) return -1; // avoid processing messages for the dialog if (!IsDialogMessage (HDialog, & msg)) { TranslateMessage ( & msg ); DispatchMessage ( & msg ); } } return (int)(msg.wParam); }

gmath.h header file:

// gmath.h #ifndef GMATH_H #define GMATH_H #include <math.h> const double PI = 3.14159265359; const double DTOR = 0.01745329251994; // degrees to radians const double RTOD = 57.29577951308; // radians to degrees // function to get the absolute value of an integer int Abs(int x) { if (x < 0) return -x; else return x; } // function to get the sign (+1 or -1) of an integer int Sign(int x) { if (x < 0) return -1; else return 1; } // a 3D vector with a homogeneous coordinate // if not used set w = 1 class Vector3 { public: double x, y, z, w; // default constructor Vector3() { x = y = z = 0.0; w = 1.0; } // set this vector to a new value void set(double x, double y, double z, double w = 1.0) { this->x = x; this->y = y; this->z = z; this->w = w; } // set this vector to a new value void set(Vector3 v) { this->x = v.x; this->y = v.y; this->z = v.z; this->w = v.w; } // scale this vector uniformly void scale(double f) { this->x *= f; this->y *= f; this->z *= f; } // return squared length of this vector double squaredLength() { return x * x + y * y + z * z; } // return length of this vector double length() { return sqrt(x * x + y * y + z * z); } // normalize this vector void normalize() { double len = length(); scale(1/len); } }; Vector3 Add(Vector3 a, Vector3 b) { // addition - returns result = a + b Vector3 result; result.x = a.x + b.x; result.y = a.y + b.y; result.z = a.z + b.z; return result; } Vector3 Subtract(Vector3 a, Vector3 b){ // subtraction - returns result = a - b Vector3 result; result.x = a.x - b.x; result.y = a.y - b.y; result.z = a.z - b.z; return result; } Vector3 CrossProduct(Vector3 a, Vector3 b) { // cross product - returns result = a X b Vector3 result; result.x = a.y * b.z - a.z * b.y; result.y = a.z * b.x - a.x * b.z; result.z = a.x * b.y - a.y * b.x; return result; } // return dot product of a & b double DotProduct(Vector3 a, Vector3 b) { return a.x * b.x + a.y * b.y + a.z * b.z; } // a 4x4 matrix class class Matrix4 { public: double m[4][4]; Matrix4(){ // default constructor set m = I m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = 0.0; m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = 0.0; m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } Matrix4(double m00, double m01, double m02, double m03, double m10, double m11, double m12, double m13, double m20, double m21, double m22, double m23, double m30, double m31, double m32, double m33) { m[0][0] = m00; m[0][1] = m01; m02 = m02; m03 = m03; m[1][0] = m10; m[1][1] = m11; m12 = m12; m13 = m13; m[2][0] = m20; m[2][1] = m21; m22 = m22; m23 = m23; m[3][0] = m30; m[3][1] = m31; m32 = m32; m33 = m33; } void makeIdMatrix() { // makes an identity matrix m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = 0.0; m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = 0.0; m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } void makeTranslationMatrix(double dx, double dy, double dz) { // makes a translation matrix m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = dx; m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = dy; m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = dz; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } void makeScaleMatrix(double sx, double sy, double sz){ // makes a scale matrix m[0][0] = sx; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = 0.0; m[1][0] = 0.0; m[1][1] = sy; m[1][2] = 0.0; m[1][3] = 0.0; m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = sz; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } // makes rotation matrix about X-axis based on a given angle in degrees void makeRotationMatrixX(double angle) { double angleInRads = angle * DTOR; makeRotationMatrixX(sin(angleInRads), cos(angleInRads)); } void makeRotationMatrixX(double sinA, double cosA){ // makes rotation matrix about X-axis m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = 0.0; m[1][0] = 0.0; m[1][1] = cosA; m[1][2] = -sinA; m[1][3] = 0.0; m[2][0] = 0.0; m[2][1] = sinA; m[2][2] = cosA; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } // makes rotation matrix about Y-axis based on a given angle in degrees void makeRotationMatrixY(double angle) { double angleInRads = angle * DTOR; makeRotationMatrixY(sin(angleInRads), cos(angleInRads)); } void makeRotationMatrixY(double sinA, double cosA){ // makes rotation matrix about Y-axis m[0][0] = cosA; m[0][1] = 0.0; m[0][2] = sinA; m[0][3] = 0.0; m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = 0.0; m[2][0] = -sinA; m[2][1] = 0.0; m[2][2] = cosA; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } // makes rotation matrix about Z-axis based on a given angle in degrees void makeRotationMatrixZ(double angle) { double angleInRads = angle * DTOR; makeRotationMatrixZ(sin(angleInRads), cos(angleInRads)); } void makeRotationMatrixZ(double sinA, double cosA){ // makes rotation matrix about Z-axis m[0][0] = cosA; m[0][1] = -sinA; m[0][2] = 0.0; m[0][3] = 0.0; m[1][0] = sinA; m[1][1] = cosA; m[1][2] = 0.0; m[1][3] = 0.0; m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; } }; // multiplies matrix m by vector a Vector3 Multiply(Matrix4 m, Vector3 a) { // returns result = m * a Vector3 result; result.x = m.m[0][0] * a.x + m.m[0][1] * a.y + m.m[0][2] * a.z + m.m[0][3] * a.w; result.y = m.m[1][0] * a.x + m.m[1][1] * a.y + m.m[1][2] * a.z + m.m[1][3] * a.w; result.z = m.m[2][0] * a.x + m.m[2][1] * a.y + m.m[2][2] * a.z + m.m[2][3] * a.w; result.w = m.m[3][0] * a.x + m.m[3][1] * a.y + m.m[3][2] * a.z + m.m[3][3] * a.w; return result; } // multiplies vector a by matrix m Vector3 Multiply(Vector3 a, Matrix4 m) { // returns result = a * m Vector3 result; result.x = a.x * m.m[0][0] + a.y * m.m[1][0] + a.z * m.m[2][0] + a.w * m.m[3][0]; result.y = a.x * m.m[0][1] + a.y * m.m[1][1] + a.z * m.m[2][1] + a.w * m.m[3][1]; result.z = a.x * m.m[0][2] + a.y * m.m[1][2] + a.z * m.m[2][2] + a.w * m.m[3][2]; result.w = a.x * m.m[0][3] + a.y * m.m[1][3] + a.z * m.m[2][3] + a.w * m.m[3][3]; return result; } // multiply x X y using loops Matrix4 Multiply(Matrix4 x, Matrix4 y) { int i, j, k; Matrix4 result; for(i=0; i < 4; i++) { for(j=0; j < 4; j++) { result.m[i][j] = 0.0; for(k=0; k < 4; k++) { result.m[i][j] += x.m[i][k] * y.m[k][j]; } } } return result; } #endif

I'd appreciate any help.