interactive drawing and 2D transformation

part 1: Specifically, you will develop an OpenGL program that allow a user to draw a circle in a position of the OpenGL window by clicking the left button of a mouse. Furthermore, your program should allow the user to draw multiple circles. When the user is done with drawing, he/she can terminate the program by entering the ’q’ or ’Q’. Your code will need to maintain a data structure to record the position of each left-click of mouse. For simplicity, you can use a 2-dimensional array, and assume that the maximum number of left-click is 100. Each time, when there is a GLUT LEFT BUTTON event, your code should insert the current mouse position to the 2-dimensional array. There are two different coordinate systems in this simple drawing. The mouse position is under the matrix coordinate system, and a vertex for drawing OpenGL geometry primitive is under the geome- try coordinate system. So your code should transform the mouse position from matrix coordinate to geometry coordinate. For simplicity, you can assume the height of the window is fixed. part 2: You will develop an OpenGL program that allow a user to perform 2D affine transformation, including translation, scaling, rotation, on a 2D object (e.g., a solid square), by selecting an transformation item from the popup menu. In this project, you can have two-layer menu as follows: • Translation – Horizontal increment – Horizontal decrement – Vertical increment – Vertical decrement • Scaling – Horizontal enlarging – Horizontal shrinking – Vertical enlarging – Vertical shrinking • Rotation – Clockwise – Counter-clockwise Your code will need to maintain several geometry parameters of an object, including horizontal and vertical translation, orientation, and scaling factors. You code should include a function (called menu), in which you should update the geometry parameters of the object. The object should be “complicated”, i.e., a composition of at least 2 OpenGL geometry primitives. The following parameters should be used for an individual 2D transformation: • 10 pixels for horizontal increment/decrement • 2 for horizontal enlarging, and 0.5 for horizontal shrinking • 20◦ for a rotation.