1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
|
/*
* Ken Shoemake's Quaternion rotation controller
*/
#include <u.h>
#include <libc.h>
#include <draw.h>
#include "dat.h"
#include "fns.h"
typedef struct Point2 Point2;
struct Point2 {
double x, y;
};
static Point2
Pt2(double x, double y)
{
return (Point2){x, y};
}
static Point2
addpt2(Point2 a, Point2 b)
{
return (Point2){a.x+b.x, a.y+b.y};
}
static Point2
subpt2(Point2 a, Point2 b)
{
return (Point2){a.x-b.x, a.y-b.y};
}
static Point2
divpt2(Point2 p, double s)
{
return (Point2){p.x/s, p.y/s};
}
static Point2 ctlcen; /* center of qball */
static double ctlrad; /* radius of qball */
static Quaternion *axis; /* constraint plane orientation, 0 if none */
static double
fmin(double a, double b)
{
return a < b? a: b;
}
/*
* Convert a mouse point into a unit quaternion, flattening if
* constrained to a particular plane.
*/
static Quaternion
mouseq(Point2 p)
{
double qx = (p.x-ctlcen.x)/ctlrad;
double qy = (p.y-ctlcen.y)/ctlrad;
double rsq = qx*qx + qy*qy;
double l;
Quaternion q;
if(rsq > 1){
rsq = sqrt(rsq);
q.r = 0;
q.i = qx/rsq;
q.j = qy/rsq;
q.k = 0;
}else{
q.r = 0;
q.i = qx;
q.j = qy;
q.k = sqrt(1-rsq);
}
if(axis != nil){
l = q.i*axis->i + q.j*axis->j + q.k*axis->k;
q.i -= l*axis->i;
q.j -= l*axis->j;
q.k -= l*axis->k;
l = sqrt(q.i*q.i + q.j*q.j + q.k*q.k);
if(l != 0){
q.i /= l;
q.j /= l;
q.k /= l;
}
}
return q;
}
void
qball(Rectangle r, Point mxy, Quaternion *orient, Quaternion *ap)
{
Quaternion down;
Point2 rmin, rmax;
Point2 rad;
if(orient == nil)
return;
axis = ap;
rmin = Pt2(r.min.x, r.min.y);
rmax = Pt2(r.max.x, r.max.y);
ctlcen = divpt2(addpt2(rmin, rmax), 2);
rad = divpt2(subpt2(rmax, rmin), 2);
ctlrad = fmin(rad.x, rad.y);
down = invq(mouseq(Pt2(mxy.x, mxy.y)));
*orient = mulq(*orient, mulq(down, mouseq(Pt2(mxy.x, mxy.y))));
}
|
