Write a function which accomplishes the task you just completed in the last exercise of week 3 (week3-10). That is, write a function

Point2D Tween(Point2D A, Point2D B, double t)

which takes two points as input, A and B, a real value for t, and then returns the point on the line through A and B for that particular value of t. Check your function by passing in points A and B as defined in exercise week3-10 and the values for t.

In exercise 3-10, we end up plotting 6 points (including the two endpoints) on the line and increment between successive values for t is 0.2. In general, if you want to plot numframes points on the line segment from point A to point B, including the two endpoints, what is the value for increment that you would use?

Suppose you have an array of points, S, which contains all the vertices of the figure your animation should start with, and a second array of points, D, which contains all the vertices of the figure which is the destination of your animation. Assume there are numpoints points in each array. Write a function, FillTween, which takes as input:

• the two arrays of points
• the value for numpoints (the number of points in each array)
• the value for t

and returns an array of points with numpoints points in it; each point calculated using corresponding points of S and D and calling the function Tween.

Now write a function, DrawSequence, which takes as input:

• the array of points to start with
• the array of points for the destination
• the number of frames you want from start to destination, inclusive (numframes)

and does the following:

for every frame to be drawn:

clears the screen;
calculates the value for t;
uses FillTween to fill a new array of points;
draws the figure, using the array of points and whatever instructions you have for how to connect the points;
swaps the buffers;

 

Do practice exercise 4.2.1 (a,b,c) on page 140 of the Hill book.

Do practice exercise 4.3.1 on page 144 of the Hill book.

Multiply the following matrices (if possible):

• [A] * [B] where [A] = [2 1 4
                                      3 7 -2
                                      1 0 5]

and [B] = [2
                 4
                 6]

• [B] * [A], where A and B are as given abovem,

What is the homogeneous scaling matrix M_S if you wish to make the object twice as wide as it is now?

What is the homogeneous scaling matrix M_S if you wish to make the object one-third as tall as it now is?