Overview

This assignment, which will be presented in stages, will play a bit with various implementations and applications of a turtle graphics system.

The Turtle

• the turtle can move forward, turn left or right, and raise or lower a pen attached to its underside.
• The position of the turtle can be described by the triple (x, y, θ):
  • (x, y) - the center of the turtle (i.e., the pen position)
  • θ - the angle the turtle is pointing at (0 towards the right/east of the surface-- as in a normal x,y coordinate system).

Part 1. A Set of Turtle Functions for OpenGL

Implement the following set of functions in OpenGL that provides turtle graphics (I've also coded it as the source file Turtle.h):

• init(x, y, theta) initializes the turtle's position and orientation
• forward(distance) - moves the turtle forward the specified distance (leving a path if the pen is lowered
• left(angle) - turn the turtle to the left the specified degrees (turning to the left increases the angle)
• right(angle) - turn the turtle to the right the specified degrees (turning to the right decreases the angle)
• penUp() - raises the pen -- turtle movemements leave no mark on the surface
• penDown() - lowers the pen -- turtle movemements leave a mark on the surface

Getting Started

• A simple approach is to allow the user to make turtle calls from the display function of an OpenGL program. I've included an example below.
• The only real issue in implementing the function is calculating the new position when executing the forward function.
  • When the turtle is facing east (angle = 0) forward movement is purely in the (positive) x direction
    • sin 0 = ?, cos 0 = ?
  • When the turtle is facing north (angle = 90 or -270) forward movement is purely in the (positive) y direction
    • sin 90 = ?, cos 90 = ?
  • When the turtle is facing west (angle = 180, or -180) forward movement is purely in the (negative) x direction
    • sin 180 = ?, cos 180 = ?
  • When the turtle is facing south (angle = 270 or -90) forward movement is purely in the (negative) y direction
    • sin 270 = ?, cos 270 = ?
  • At all other angles, the movement is partially in the x and partially in the y direction.
    • Here is an image of two lines of length 1 in the first quadrant
      
      • Go back to your basic trigonometry, and relate the x and y components of the lines to sin and cos
    • Now figure out given a line length other than 1 the change in x and y
    • The signs of the changes in x and y will work themselves out OK, as you can see from the movements along the axes.

A Simple Turtle Application Program

#define GLUT_DISABLE_ATEXIT_HACK
#include 

#include 
#include 

#include "Turtle.h"

using namespace std;

void init() {
    glClearColor(1, 1, 1, 1);
    gluOrtho2D(-100, 100, -100, 100);
}

static void display(void) {
    glClear (GL_COLOR_BUFFER_BIT);
    glColor3f (1.0, 0.0, 0.0);

    init(0, 0, 0);

    penUp();
    forward(25);
    penDown();
    left(90);
    forward(25);
    left(90);
    forward(50);
    left(90);
    forward(50);
    left(90);
    forward(50);
    left(90);
    forward(25);
}

int main(int argc, char *argv[]) {
    glutInit(&argc, argv);
    glutInitWindowPosition (0, 0);
    glutInitWindowSize (200, 200);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
    glutCreateWindow ("Turtle");

    glutDisplayFunc(display);

    init();

    glutMainLoop();

    return 0;
}
			

Some More Implementation Details

• In your Turtle.cpp file, have (file scope, i.e., global) variablkes corresponding to the
  • current position (x and y coordinates) of the turtle
  • current angle of the turtle
  • Whether the pen is up or down
• The init function accepts initial settings for the position and angle (you might also choose to allow the init function to accept an initial up/down position for the pen).
• The left/right functions increase/decrease the value of the current angle by the parameter (you might consider using the % operator to keep the angle value within the 360 degree range).
• The function moves the turtle to a new position. If the pen is up this simply changes the current position of the turtle, however, if the pen is down, the turtle draws a straght line between the original and new positions.
  • Drawing the path is achieved by a pair of glVertex calls within a glBegin/glEnd block with a GL_LINES value).
• Given a current angle of theta, and a distance (the parameter to forward)
  • the movement in the x direction is distance * cos(theta)
  • the movement in the x direction is distance * sin(theta)
  • The C++ cos and sin functions accept radians as their arguments. To convert your angle values to radians, multiply the angle value by π/180.0 (there are π radians in 180 degrees; thus one degree is equal to π/180.0 radians).

Part 2 - A More Complex Turtle Image

Write a turtle app that reproduces the above image (it doesn't have to be exact). (Click the picture to see the Wiki picture page -- it also contains pseudocode for the spiral-- you can either try to decipher it, or alternatively, examine the image and figure out how to reproduce it.)

Here is my quick and dirty attempt:

Files for Assignment 2