Creating animations using Transformations in OpenGL

Last Updated : 19 Sep, 2023

Animation is the illusion of making us think that an object is really moving on the screen. But underneath they are just complex algorithms updating and drawing different objects.

Aim: A complex animation of a walking dinosaur in 2D. Method: Using Transformations of individual body parts. See this Video:

In OPENGL.

Algorithm

There are 3 main transformations in Computer Graphics - Translation, Rotation and Scaling. All can be implemented using very simple mathematics.

Translation: X = x + tx,    tx is the amount of translation in x-axis
             Y = y + ty,    ty is the amount of translation in y-axis

Rotation: X = xcosA - ysinA,   A is the angle of rotation.
          Y = xsinA + ycosA

Scaling: X = x*Sx,      Sx is Scaling Factor
         Y = y*Sy,    Sy is Scaling Factor

For drawing figures, Bresenham's Line drawing algorithm will be used together with the above equations to draw each line according to need.

Implementation

The body of the dinosaur is split up into 8 main portions - Head, upperBody, Tail, downBody, and the four legs The parts are stores as text files with comma separated coordinates, which are imported during running of the program:

The centres of rotation of each object were stored in a separate file:

centrePts

Since, all files were created by hand, there was room for little errors which were corrected in the following file:

offsetDino

Note: Please download all the above files before running the program and keep in the same directory. Each one will have its own object storing the following:

All the lines of the object in a big array
The number of lines
The current amount of translation
The centre of rotation
The offsets
The current amount of rotation
The direction of rotation

The program will work in the following order:

THe OpenGL window will start
All the files will be read and stored in their respective objects
An infinite while loop will be started
The screen will be cleared
A line will be drawn depicting the grassland
All the parts will be updated
All the parts will be drawn
The body translation value will be decremented, and if the dinosaur is out of the window, it will be reset.
The loop will go to its next iteration

During updation of an object, the rotationstate is checked and if it is overshooting the threshold of rotation, then the direction of rotation is reversed. The rotationstate is 0 if it is not to be rotated.

#include <stdio.h>
#include <GL/glut.h>
#include <math.h>

// these are the parameters
#define maxHt 800
#define maxWd 600
#define maxLns 10000
#define transSpeed 1
#define rotSpeed 0.02
#define rotateLimit 0.2
#define boundLimitL -200
#define boundLimitR 500
#define grasslandy 230

// Structure for storing lines
typedef struct lines {
    int x1, x2, y1, y2;
} LINE;

// Object type structure for storing each body part
typedef struct objects {
    LINE edge[maxLns];
    int translation, cx, cy, xoffset, yoffset;
    float theta;
    int rotationState;
    int EdgeCount;
} Object;

// the different objects
Object Head, upBody, Tail, downBody, FlegF, FlegB, BlegF, BlegB;
// global
int dinoTranslate = 0;

// basic init function for OPENGL
void myInit(void)
{
    glClearColor(1.0, 1.0, 1.0, 0.0);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0, maxHt, 0, maxWd);
    glClear(GL_COLOR_BUFFER_BIT);
}

// this function translates, and rotates a point according to an object and draws it
void rotateandshiftPt(int px, int py, Object obbj)
{
    int xf, yf;

    xf = obbj.cx + (int)((float)(px - obbj.cx) * cos(obbj.theta)) - ((float)(py - obbj.cy) * sin(obbj.theta));
    yf = obbj.cy + (int)((float)(px - obbj.cx) * sin(obbj.theta)) + ((float)(py - obbj.cy) * cos(obbj.theta));
    glBegin(GL_POINTS);
    glVertex2i(obbj.translation + xf + obbj.xoffset, yf + obbj.yoffset);
    glEnd();
}

// this function draws a line using Bresenhams
void drawLineBresenham(int x1, int y1, int x2, int y2, Object obbj)
{
    int Dx, Dy, Dxmul2, Dymul2, Pk, xtempi, ytempi;
    float lineSlope, xtemp, ytemp;
    Dx = abs(x2 - x1);
    Dy = abs(y2 - y1);
    Dxmul2 = 2 * Dx;
    Dymul2 = 2 * Dy;
    ytemp = (float)(y2 - y1);
    xtemp = (float)(x2 - x1);
    lineSlope = (ytemp / xtemp);

    if (lineSlope >= -1.0 && lineSlope <= 1.0) {
        Pk = Dymul2 - Dx;
        if (x1 > x2) {
            xtempi = x2;
            x2 = x1;
            x1 = xtempi;
            ytempi = y2;
            y2 = y1;
            y1 = ytempi;
        }
        for (xtempi = x1, ytempi = y1; xtempi <= x2; xtempi++) {
            rotateandshiftPt(xtempi, ytempi, obbj);
            if (Pk < 0) {
                Pk = Pk + Dymul2;
            } else {
                Pk = Pk + Dymul2 - Dxmul2;
                if (lineSlope >= 0.0 && lineSlope <= 1.0)
                    ytempi = ytempi + 1;
                else if (lineSlope < 0.0 && lineSlope >= -1.0)
                    ytempi = ytempi - 1;
            }
        }
    } else {
        Pk = Dxmul2 - Dy;
        if (y1 > y2) {
            xtempi = x2;
            x2 = x1;
            x1 = xtempi;
            ytempi = y2;
            y2 = y1;
            y1 = ytempi;
        }
        for (xtempi = x1, ytempi = y1; ytempi <= y2; ytempi++) {
            rotateandshiftPt(xtempi, ytempi, obbj);
            if (Pk < 0) {
                Pk = Pk + Dxmul2;
            } else {
                Pk = Pk + Dxmul2 - Dymul2;
                if (lineSlope > 1.0)
                    xtempi = xtempi + 1;
                else if (lineSlope < -1.0)
                    xtempi = xtempi - 1;
            }
        }
    }
}
// here all the edges are iterated and drawn
void drawObj(Object obbj)
{
    int i;
    for (i = 0; i < obbj.EdgeCount; i++) {
        drawLineBresenham(obbj.edge[i].x1, obbj.edge[i].y1, obbj.edge[i].x2, obbj.edge[i].y2, obbj);
    }
}

// in this function, an object is updated
void updateObj(Object* obbj)
{
    obbj->translation = dinoTranslate;

    if (obbj->rotationState == 1) {
        obbj->theta = obbj->theta + rotSpeed;
        if (obbj->theta >= (3.14159))
            obbj->theta = obbj->theta - (2.0 * 3.14159);
        if (obbj->theta > rotateLimit)
            obbj->rotationState = -1;

    } else if (obbj->rotationState == -1) {
        obbj->theta = obbj->theta - rotSpeed;

        if (obbj->theta <= (-3.14159))
            obbj->theta = (2.0 * 3.14159) + obbj->theta;

        if (obbj->theta < -rotateLimit)
            obbj->rotationState = 1;
    }
}

// The actual function where the Dinosaur is drawn
void drawDino(void)
{
    // an infinite while loop for moving the dinosaur
    while (1) {
        glClear(GL_COLOR_BUFFER_BIT);
        // draw grassland
        glLineWidth(5.0);
        glColor3f(0.0f, 1.0f, 0.3f);
        glBegin(GL_LINES);
        glVertex2i(0, grasslandy);
        glVertex2i(maxHt, grasslandy);
        glEnd();
        glPointSize(3.0);
        glColor3f(0.9f, 0.5f, 0.6f);
        // update all parts

        updateObj(&Head);
        updateObj(&upBody);
        updateObj(&Tail);
        updateObj(&downBody);
        updateObj(&FlegF);
        updateObj(&FlegB);
        updateObj(&BlegF);
        updateObj(&BlegB);

        // draw all parts, also draw joining parts
        drawObj(Head);
        drawObj(upBody);
        drawObj(Tail);
        drawObj(downBody);
        drawObj(FlegF);
        drawObj(FlegB);
        drawObj(BlegF);
        drawObj(BlegB);

        dinoTranslate--; // decreased because moving forward
        if (dinoTranslate <= boundLimitL) {
            dinoTranslate = boundLimitR;
            printf("\ntranslate %d", dinoTranslate);
        }
        printf("\ntranslate %d", dinoTranslate);
        glFlush();
    }
}

// TAn object is stored using this function
void storeObj(char* str, Object* obbj)
{
    obbj->theta = 0.0;

    FILE* fp;
    fp = fopen(str, "r");
    if (fp == NULL) {
        printf("Could not open file");
        return;
    }
    obbj->EdgeCount = 0;
    int count = 0, x1, y1, x2, y2;
    while (!feof(fp)) {
        count++;
        if (count > 2) {
            x1 = x2;
            y1 = y2;
            count = 2;
        }
        if (count == 1) {
            fscanf(fp, "%d, %d", &x1, &y1);
        } else {
            fscanf(fp, "%d, %d", &x2, &y2);
            printf("\n%d, %d", x2, y2);
            obbj->edge[obbj->EdgeCount].x1 = x1;
            obbj->edge[obbj->EdgeCount].y1 = y1;
            obbj->edge[obbj->EdgeCount].x2 = x2;
            obbj->edge[obbj->EdgeCount].y2 = y2;
            obbj->EdgeCount++;
        }
    }

    // printf("\nPolygon stored!");
    fclose(fp);
}

// All parts are stored.
void storeAllParts()
{
    FILE* fp, *fp2;
    int cx, cy;
    fp = fopen("centrePts.txt", "r");
    fp2 = fopen("offsetDino.txt", "r");
    if (fp == NULL || fp2 == NULL) {
        printf("Could not open file");
        return;
    }
    // parts
    //----------------
    // head+neck
    storeObj("headDino.txt", &Head);
    fscanf(fp, "%d, %d", &cx, &cy);
    Head.cx = cx;
    Head.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    Head.xoffset = cx;
    Head.yoffset = cy;
    Head.rotationState = 1;

    // upper body boundary(only translation)
    storeObj("bodyupDino.txt", &upBody);
    upBody.cx = 0;
    upBody.cy = 0;
    fscanf(fp2, "%d, %d", &cx, &cy);
    upBody.xoffset = cx;
    upBody.yoffset = cy;
    upBody.rotationState = 0;

    // tail
    storeObj("tailDino.txt", &Tail);
    fscanf(fp, "%d, %d", &cx, &cy);
    Tail.cx = cx;
    Tail.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    Tail.xoffset = cx;
    Tail.yoffset = cy;
    Tail.rotationState = -1;

    // back leg front
    storeObj("backlegFDino.txt", &BlegF);
    fscanf(fp, "%d, %d", &cx, &cy);
    BlegF.cx = cx;
    BlegF.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    BlegF.xoffset = cx;
    BlegF.yoffset = cy;
    BlegF.rotationState = -1;

    // back leg rear
    storeObj("backlegRDino.txt", &BlegB);
    fscanf(fp, "%d, %d", &cx, &cy);
    BlegB.cx = cx;
    BlegB.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    BlegB.xoffset = cx;
    BlegB.yoffset = cy;
    BlegB.rotationState = 1;

    // lower body boundary(only translation)
    storeObj("bodydownDino.txt", &downBody);
    downBody.cx = 0;
    downBody.cy = 0;
    fscanf(fp2, "%d, %d", &cx, &cy);
    downBody.xoffset = cx;
    downBody.yoffset = cy;
    downBody.rotationState = 0;

    // front leg rear
    storeObj("frontlegRDino.txt", &FlegB);
    fscanf(fp, "%d, %d", &cx, &cy);
    FlegB.cx = cx;
    FlegB.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    FlegB.xoffset = cx;
    FlegB.yoffset = cy;
    FlegB.rotationState = -1;

    // front leg front
    storeObj("frontlegFDino.txt", &FlegF);
    fscanf(fp, "%d, %d", &cx, &cy);
    FlegF.cx = cx;
    FlegF.cy = cy;
    fscanf(fp2, "%d, %d", &cx, &cy);
    FlegF.xoffset = cx;
    FlegF.yoffset = cy;
    FlegF.rotationState = 1;

    //------------------------
    fclose(fp);
}

void main(int argc, char** argv)
{

    storeAllParts();
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
    glutInitWindowSize(maxHt, maxWd);
    glutInitWindowPosition(0, 0);
    glutCreateWindow("Walking dinosaur");
    myInit();
    glutDisplayFunc(drawDino); // actual loop call
    glutMainLoop();
}