Project 5. Due Friday 2 October.

As always, each plot must have your name in the title, the axis
labeled and the collection of plots must be stapled. The maple
help page which is most on target can be called up with ?plot[structure]

The goal of this project is to draw five pictures using maple, four
of which are the pictures on page 761 of the text. This requires doing
some fancier footwork than we have done before. We need to use PLOT
(which is different from plot).

start with the with(plots): command.

Try these (you can use "cut and paste" to save typing them)
poly1:=[[-1,-1],[1,2],[1,-1]];
poly2:=[[0,0],[2,1],[1,-1]];
PLOT(POLYGONS(poly1,poly2,COLOR(RGB,0.7,0.7,0.7,0.4,0.4,0.4)));
PLOT(POLYGONS(poly2,poly1,COLOR(RGB,0.7,0.7,0.7,0.4,0.4,0.4)));

Note that the ploygons are listed from front to back. The color
command is using RGB, or red-green-blue mixtures. The first polygon
is using 0.7,0.7,0.7 or 70% each of red, green and blue. the second
polygon uses the 0.4,0.4,0.4 numbers, or 40% of each. Mixtures
with equal amounts of each color are grays. The 70% is a lighter
grey then the 40% grey. (The colors add rather than subtract as in
painting.) It you have access to a color monitor try using
1,0,0 (red), 0,1,0 (green) or even 0.1,0.6,0.2 (a different green)

#1. Produce Figure 2 on page 761, namely the graph of x+y+1>=0 with
the dotted line x=1. Here is help how to add a dotted line and the
title. (Note that you need to figure out the co-ordinates of the
corners of the trapazoid.)

PLOT( POLYGONS( poly2,poly1,COLOR(RGB,0.7,0.7,0.7,0.4,0.4,0.4) ),
CURVES( [[0,-1],[0.5,2]],LINESTYLE(2) ),
TITLE(`help from the good doctor`),
AXESLABELS(`x`,`y`));

#2 We will do Figure 3 in two steps. POLYGONS can only be convex
and the region in Figure 3 is non-convex. This plot will draw the
convex "hole" x>=y^2. So we need to fill in a curved region. Well
a curved region is easily approximated by a polygon with a number
of edges. For example here is the region under y=sin x, x=0..Pi.
(Note the problem with sinploy, evalf forces maple to change the
symbols into floats (EVALuate to Float), float is another term
for decimal number approximations)

n:=20;
sinpoly:=[seq([Pi*i/n,sin(Pi*i/n)],i=0..n)];
sinpoly2:=[seq([evalf(Pi*i/n),evalf(sin(Pi*i/n))],i=0..n)];
PLOT(POLYGONS(sinpoly2,COLOR(RGB,0.5,0.5,0.5)));

Your job is to draw the hole, the region x>=y^2.

#3 Draw the concave region x<=y^2 as in Figure 3 on page 761. Draw
the rectanglar big region and then draw x>=y^2 in the background
color so it looks like the piece is missing.

#4 Draw Figure 5, using PLOT3D and a 3D triangle, (each co-ordinate
of the polygon will have 3 entries), a STYLE(PATCH) will fill the
triangle. Include the (normal) axes.

#5 The hard one is to draw something like figure 4. For now lets
just assume D is the region { (x,y): 0<=x<=1, 0<=y<=2 } and
f(x,y) is the function 1 - ((y-1)^2)/3 - x/20. The MESH command is
helpful as is 

mesh:=[seq([seq([i/n,2*j/m,f(i/n,2*j/n)],i=0..n)],j=0..m)]

(POLYGONS have to be planar, so you cannot use it to draw f.)
Include the (normal) axes.