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:
- headDino
- PolyDino
- tailDino
- backlegFDino
- backlegRDino
- bodydownDino
- bodyupDino
- frontlegFDino
- frontlegRDino
The centres of rotation of each object were stored in a separate file:
Since, all files were created by hand, there was room for little errors which were corrected in the following file:
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();
} |
Output: This is a sample screenshot:
Don’t forget to download the files before running the program.