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-rw-r--r--common/algebra.cpp235
1 files changed, 224 insertions, 11 deletions
diff --git a/common/algebra.cpp b/common/algebra.cpp
index a34f91d..05a357c 100644
--- a/common/algebra.cpp
+++ b/common/algebra.cpp
@@ -26,10 +26,11 @@ void Matrix44::CreateLookAt(const Point3& Eye, const Point3& Target, const Vecto
y.Normalize();
z.Normalize();
- m_Rows[0] = Float4(x.GetX(), y.GetX(), z.GetX(), 0.0f);
- m_Rows[1] = Float4(x.GetY(), y.GetY(), z.GetY(), 0.0f);
- m_Rows[2] = Float4(x.GetZ(), y.GetZ(), z.GetZ(), 0.0f);
+ m_Rows[0] = Vector4(x.GetX(), y.GetX(), z.GetX(), 0.0f);
+ m_Rows[1] = Vector4(x.GetY(), y.GetY(), z.GetY(), 0.0f);
+ m_Rows[2] = Vector4(x.GetZ(), y.GetZ(), z.GetZ(), 0.0f);
m_Rows[3] = m_Rows[0]*-Eye.GetX() + m_Rows[1]*-Eye.GetY() + m_Rows[2]*-Eye.GetZ();
+ m_Rows[3][3] = 1.0f;
}
void Matrix44::CreatePerspective(float FoVy, float Aspect, float Near, float Far)
@@ -54,21 +55,134 @@ void Matrix44::CreatePerspective(float FoVy, float Aspect, float Near, float Far
c = -(Far + Near) / (Far - Near);
d = -(2.0f * Far * Near) / (Far - Near);
- m_Rows[0] = Float4(x, 0, a, 0);
- m_Rows[1] = Float4(0, y, b, 0);
- m_Rows[2] = Float4(0, 0, c, d);
- m_Rows[3] = Float4(0, 0, -1, 0);
+ m_Rows[0] = Vector4(x, 0, 0, 0);
+ m_Rows[1] = Vector4(0, y, 0, 0);
+ m_Rows[2] = Vector4(a, b, c, -1);
+ m_Rows[3] = Vector4(0, 0, d, 0);
+}
+
+// Inverse code from the GLU library.
+Matrix44 Inverse(const Matrix44& m)
+{
+#define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
+#define MAT(m,c,r) m.m_Rows[r][c]
+
+ float wtmp[4][8];
+ float m0, m1, m2, m3, s;
+ float *r0, *r1, *r2, *r3;
+
+ r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
+
+ r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
+ r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
+ r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
+
+ r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
+ r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
+ r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
+
+ r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
+ r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
+ r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
+
+ r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
+ r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
+ r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
+
+ // choose pivot - or die
+ if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
+ if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
+ if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
+// if (0.0 == r0[0]) return GL_FALSE;
+
+ // eliminate first variable
+ m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
+ s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
+ s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
+ s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
+ s = r0[4];
+ if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
+ s = r0[5];
+ if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
+ s = r0[6];
+ if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
+ s = r0[7];
+ if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
+
+ // choose pivot - or die
+ if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
+ if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
+// if (0.0 == r1[1]) return GL_FALSE;
+
+ // eliminate second variable
+ m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
+ r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
+ r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
+ s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
+ s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
+ s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
+ s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
+
+ // choose pivot - or die
+ if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
+// if (0.0 == r2[2]) return GL_FALSE;
+
+ // eliminate third variable
+ m3 = r3[2]/r2[2];
+ r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
+ r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
+ r3[7] -= m3 * r2[7];
+
+ // last check
+// if (0.0 == r3[3]) return GL_FALSE;
+
+ s = 1.0f/r3[3]; // now back substitute row 3
+ r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
+
+ m2 = r2[3]; // now back substitute row 2
+ s = 1.0f/r2[2];
+ r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
+ r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
+ m1 = r1[3];
+ r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
+ r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
+ m0 = r0[3];
+ r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
+ r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
+
+ m1 = r1[2]; // now back substitute row 1
+ s = 1.0f/r1[1];
+ r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
+ r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
+ m0 = r0[2];
+ r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
+ r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
+
+ m0 = r0[1]; // now back substitute row 0
+ s = 1.0f/r0[0];
+ r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
+ r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
+
+ Matrix44 out(Vector4(r0[4], r1[4], r2[4], r3[4]),
+ Vector4(r0[5], r1[5], r2[5], r3[5]),
+ Vector4(r0[6], r1[6], r2[6], r3[6]),
+ Vector4(r0[7], r1[7], r2[7], r3[7]));
+
+ return out;
+
+#undef MAT
+#undef SWAP_ROWS
}
// ============================================================================
-// Other Functions.
+// Project/Unproject a point.
-// Convert object coordinates to screen coordinates.
+// Convert world coordinates to screen coordinates.
Point3 ProjectPoint(const Point3& Pt, const Matrix44& ModelView, const Matrix44& Projection, const int Viewport[4])
{
- Point3 Tmp;
+ Vector4 Tmp;
- Tmp = Pt * ModelView;
+ Tmp = Vector4(Pt) * ModelView;
Tmp = Tmp * Projection;
// Normalize.
@@ -77,3 +191,102 @@ Point3 ProjectPoint(const Point3& Pt, const Matrix44& ModelView, const Matrix44&
// Screen coordinates.
return Point3(Viewport[0]+(1+Tmp[0])*Viewport[2]/2, Viewport[1]+(1+Tmp[1])*Viewport[3]/2, (1+Tmp[2])/2);
}
+
+// Convert screen coordinates to world coordinates.
+Point3 UnprojectPoint(const Point3& Point, const Matrix44& ModelView, const Matrix44& Projection, const int Viewport[4])
+{
+ Point3 Tmp = Point;
+ UnprojectPoints(&Tmp, 1, ModelView, Projection, Viewport);
+ return Tmp;
+}
+
+void UnprojectPoints(Point3* Points, int NumPoints, const Matrix44& ModelView, const Matrix44& Projection, const int Viewport[4])
+{
+ // Calculate the screen to model transform.
+ Matrix44 Transform = Inverse(ModelView * Projection);
+
+ for (int i = 0; i < NumPoints; i++)
+ {
+ Vector4 Tmp;
+
+ // Convert the point to homogeneous coordinates.
+ Tmp[0] = (Points[i][0] - Viewport[0]) * 2.0f / Viewport[2] - 1.0f;
+ Tmp[1] = (Points[i][1] - Viewport[1]) * 2.0f / Viewport[3] - 1.0f;
+ Tmp[2] = Points[i][2] * 2.0f - 1.0f;
+ Tmp[3] = 1.0f;
+
+ Tmp = Tmp * Transform;
+
+ if (Tmp[3] != 0.0f)
+ Tmp /= Tmp[3];
+
+ Points[i] = Point3(Tmp[0], Tmp[1], Tmp[2]);
+ }
+}
+
+// ============================================================================
+// Geometry functions.
+
+// Sutherland-Hodgman method of clipping a polygon to a plane.
+void PolygonPlaneClip(Point3* InPoints, int NumInPoints, Point3* OutPoints, int* NumOutPoints, const Vector4& Plane)
+{
+ Point3 *s, *p, i;
+
+ *NumOutPoints = 0;
+ s = &InPoints[NumInPoints-1];
+
+ for (int j = 0; j < NumInPoints; j++)
+ {
+ p = &InPoints[j];
+
+ if (Dot3(*p, Plane) + Plane[3] <= 0)
+ {
+ if (Dot3(*s, Plane) + Plane[3] <= 0)
+ {
+ // Both points inside.
+ OutPoints[*NumOutPoints] = *p;
+ *NumOutPoints = *NumOutPoints + 1;
+ }
+ else
+ {
+ // Outside, inside.
+ LinePlaneIntersection(i, *s, *p, Plane);
+
+ OutPoints[*NumOutPoints] = i;
+ *NumOutPoints = *NumOutPoints + 1;
+ OutPoints[*NumOutPoints] = *p;
+ *NumOutPoints = *NumOutPoints + 1;
+ }
+ }
+ else
+ {
+ if (Dot3(*s, Plane) + Plane[3] <= 0)
+ {
+ // Inside, outside.
+ LinePlaneIntersection(i, *s, *p, Plane);
+
+ OutPoints[*NumOutPoints] = i;
+ *NumOutPoints = *NumOutPoints + 1;
+ }
+ }
+
+ s = p;
+ }
+}
+
+// Return the intersction point of a line and a plane, or false if they are parallel.
+bool LinePlaneIntersection(Point3& Intersection, const Point3& Start, const Point3& End, const Vector4& Plane)
+{
+ Vector3 Dir = End - Start;
+
+ float t1 = Dot3(Plane, Start) + Plane[3];
+ float t2 = Dot3(Plane, Dir);
+
+ if (t2 == 0.0f)
+ return false;
+
+ Intersection = Start - (t1 / t2) * Dir;
+
+ return true;
+}
+