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#1 stretch  Icon User is offline

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Rotating Triangle

Posted 18 June 2011 - 08:15 PM

I am working on a program that rotates a triangle on one of its axis. I have everything else to work but I have not been able to get it to work properly. I have tried to modify the tIn and tOut with the axis and it has no effect. I have also tried to modify the rotation matrix. It gave me some results but not what I was wanting.
/*
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, tIn, tOut;                         // 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(  50,   50, 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);
	tIn.makeTranslationMatrix(-pts[2].x,-pts[2].y,-pts[2].z);// 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);

    tOut.makeTranslationMatrix(pts[2].x,pts[2].y,pts[2].z);// 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);
}


Here is the 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

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Replies To: Rotating Triangle

#2 ishkabible  Icon User is offline

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Re: Rotating Triangle

Posted 18 June 2011 - 09:05 PM

TL;DR your code, sorry im tired.
however i have some advice.
simple math for this problem, matrices are not needed.

xPrime = cos(theta) * x - sin(theta) * y;
yPrime = sin(theta) * x + cos(theta) * y;



just my 2 cents

This post has been edited by ishkabible: 18 June 2011 - 09:07 PM

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#3 stretch  Icon User is offline

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Re: Rotating Triangle

Posted 18 June 2011 - 09:29 PM

For this program I have to use the matrix. Thank you for trying to help though. I think I might be missing a line somewhere around this part but unsure what it is.
 tIn.makeTranslationMatrix(-pts[2].x,-pts[2].y,-pts[2].z);// make the current rotation matrix  

078     rz.makeRotationMatrixZ(angle);  

079        

080        

081        

082        

083     // update the composite matrix - remember we must pre-multiply by m: c = m x c  

084     c = Multiply(rz, c);  

085    

086     tOut.makeTranslationMatrix(pts[2].x,pts[2].y,pts[2].z);//  


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