33
what the heck? this is not even close!
34
or so it looks. check again and you'll notice the bounds of the circle are the same as the bounds of the x axis. but why isn't it exactly equal? aren't we following the x axis?
35
well, it is true that we're following the x axis, but we have to remember we are also following the y axis. this circle is defined on the xy plane, which means we have to find the coefficients of y as well.
36
before i show you, try for a bit to see if you can get them yourself!
37
38
39
40
41
42
43
44
45
if you tried, that's cool, if you didn't, that's a little less cool but still acceptable. we're still learning!
46
47
these are the coefficients. but what do we do now? we have them both separate, but we want one that covers the plane, and is actually 3 dimensional looking.
48
luckily, this part is a lot easier than it seems. all we need to do is put the products together. remember that we've been multiplying these coefficients by either cos(2pi*t) or sin(2pi*t). this has to come with the coefficients.
49
50
now we know how to project any point on the (x,y) plane! if we wanted to project (0.3,0.2), we would just replace our c_x and c_y values.
51
52
but what about 3d? what about the z axis?
53
you're in luck! this part is actually easier than the (x,y) plane.
54
55
notice what happens to this point as we drag our xy rotation.
56
absolutely nothing! it stays fixed at zero, so we already have our first coefficient, zero.
57
but what about the y value? well, it's only dependent on the xz rotation, and when that is zero, the point is at one. you know what that means!
58
59
our last coefficient is cos(r_xz). now we can write a formula for projection!
60
61
don't worry if this looks complicated! it's just everything we've done compressed into one line that you can input coordinates into.
62
63
what about functions though? well, that's the next section!
64
functions
65
behind the scenes
86
95
obsługiwane przez
obsługiwane przez
Nowy pusty wykres
Przykłady