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
109
110
111
112
113
114
|
// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5IntrLine2Circle2.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrLine2Circle2<Real>::IntrLine2Circle2 (const Line2<Real>& line,
const Circle2<Real>& circle)
:
mLine(&line),
mCircle(&circle)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line2<Real>& IntrLine2Circle2<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Circle2<Real>& IntrLine2Circle2<Real>::GetCircle () const
{
return *mCircle;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine2Circle2<Real>::Find ()
{
Real t[2];
bool intersects = Find(mLine->Origin, mLine->Direction,
mCircle->Center, mCircle->Radius, mQuantity, t);
if (intersects)
{
for (int i = 0; i < mQuantity; ++i)
{
mPoint[i] = mLine->Origin + t[i]*mLine->Direction;
}
}
mIntersectionType = (mQuantity > 0 ? IT_POINT : IT_EMPTY);
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrLine2Circle2<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector2<Real>& IntrLine2Circle2<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine2Circle2<Real>::Find (const Vector2<Real>& origin,
const Vector2<Real>& direction, const Vector2<Real>& center,
Real radius, int& rootCount, Real t[2])
{
// Intersection of a the line P+t*D and the circle |X-C| = R. The line
// direction is unit length. The t value is a root to the quadratic
// equation:
// 0 = |t*D+P-C|^2 - R^2
// = t^2 + 2*Dot(D,P-C)*t + |P-C|^2-R^2
// = t^2 + 2*a1*t + a0
// If two roots are returned, the order is T[0] < T[1].
Vector2<Real> diff = origin - center;
Real a0 = diff.SquaredLength() - radius*radius;
Real a1 = direction.Dot(diff);
Real discr = a1*a1 - a0;
if (discr > Math<Real>::ZERO_TOLERANCE)
{
rootCount = 2;
discr = Math<Real>::Sqrt(discr);
t[0] = -a1 - discr;
t[1] = -a1 + discr;
}
else if (discr < -Math<Real>::ZERO_TOLERANCE)
{
rootCount = 0;
}
else // discr == 0
{
rootCount = 1;
t[0] = -a1;
}
return rootCount != 0;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrLine2Circle2<float>;
template WM5_MATHEMATICS_ITEM
class IntrLine2Circle2<double>;
//----------------------------------------------------------------------------
}
|
