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+/**
+ @file Vector3.cpp
+
+ 3D vector class
+
+ @maintainer Morgan McGuire, http://graphics.cs.williams.edu
+
+ @cite Portions based on Dave Eberly's Magic Software Library at http://www.magic-software.com
+
+ @created 2001-06-02
+ @edited 2009-11-27
+ */
+
+#include <limits>
+#include <stdlib.h>
+#include "G3D/Vector3.h"
+#include "G3D/g3dmath.h"
+#include "G3D/stringutils.h"
+#include "G3D/BinaryInput.h"
+#include "G3D/BinaryOutput.h"
+#include "G3D/TextInput.h"
+#include "G3D/TextOutput.h"
+#include "G3D/Vector3int16.h"
+#include "G3D/Matrix3.h"
+#include "G3D/Vector2.h"
+#include "G3D/Color3.h"
+#include "G3D/Vector4int8.h"
+#include "G3D/Vector3int32.h"
+#include "G3D/Any.h"
+
+namespace G3D {
+
+Vector3::Vector3(const Any& any) {
+ any.verifyName("Vector3");
+ any.verifyType(Any::TABLE, Any::ARRAY);
+ any.verifySize(3);
+
+ if (any.type() == Any::ARRAY) {
+ x = any[0];
+ y = any[1];
+ z = any[2];
+ } else {
+ // Table
+ x = any["x"];
+ y = any["y"];
+ z = any["z"];
+ }
+}
+
+Vector3::operator Any() const {
+ Any any(Any::ARRAY, "Vector3");
+ any.append(x, y, z);
+ return any;
+}
+
+Vector3::Vector3(const class Color3& v) : x(v.r), y(v.g), z(v.b) {}
+
+Vector3::Vector3(const class Vector3int32& v) : x((float)v.x), y((float)v.y), z((float)v.z) {}
+
+Vector3::Vector3(const Vector4int8& v) : x(v.x / 127.0f), y(v.y / 127.0f), z(v.z / 127.0f) {}
+
+Vector3::Vector3(const class Vector2& v, float _z) : x(v.x), y(v.y), z(_z) {
+}
+
+Vector3& Vector3::ignore() {
+ static Vector3 v;
+ return v;
+}
+
+const Vector3& Vector3::zero() { static const Vector3 v(0, 0, 0); return v; }
+const Vector3& Vector3::one() { static const Vector3 v(1, 1, 1); return v; }
+const Vector3& Vector3::unitX() { static const Vector3 v(1, 0, 0); return v; }
+const Vector3& Vector3::unitY() { static const Vector3 v(0, 1, 0); return v; }
+const Vector3& Vector3::unitZ() { static const Vector3 v(0, 0, 1); return v; }
+const Vector3& Vector3::inf() { static const Vector3 v((float)G3D::finf(), (float)G3D::finf(), (float)G3D::finf()); return v; }
+const Vector3& Vector3::nan() { static const Vector3 v((float)G3D::fnan(), (float)G3D::fnan(), (float)G3D::fnan()); return v; }
+const Vector3& Vector3::minFinite(){ static const Vector3 v(-FLT_MAX, -FLT_MAX, -FLT_MAX); return v; }
+const Vector3& Vector3::maxFinite(){ static const Vector3 v(FLT_MAX, FLT_MAX, FLT_MAX); return v; }
+
+Vector3::Axis Vector3::primaryAxis() const {
+
+ Axis a = X_AXIS;
+
+ double nx = abs(x);
+ double ny = abs(y);
+ double nz = abs(z);
+
+ if (nx > ny) {
+ if (nx > nz) {
+ a = X_AXIS;
+ } else {
+ a = Z_AXIS;
+ }
+ } else {
+ if (ny > nz) {
+ a = Y_AXIS;
+ } else {
+ a = Z_AXIS;
+ }
+ }
+
+ return a;
+}
+
+
+size_t Vector3::hashCode() const {
+ unsigned int xhash = (*(int*)(void*)(&x));
+ unsigned int yhash = (*(int*)(void*)(&y));
+ unsigned int zhash = (*(int*)(void*)(&z));
+
+ return xhash + (yhash * 37) + (zhash * 101);
+}
+
+std::ostream& operator<<(std::ostream& os, const Vector3& v) {
+ return os << v.toString();
+}
+
+
+//----------------------------------------------------------------------------
+
+double frand() {
+ return rand() / (double) RAND_MAX;
+}
+
+Vector3::Vector3(TextInput& t) {
+ deserialize(t);
+}
+
+Vector3::Vector3(BinaryInput& b) {
+ deserialize(b);
+}
+
+
+Vector3::Vector3(const class Vector3int16& v) {
+ x = v.x;
+ y = v.y;
+ z = v.z;
+}
+
+
+void Vector3::deserialize(BinaryInput& b) {
+ x = b.readFloat32();
+ y = b.readFloat32();
+ z = b.readFloat32();
+}
+
+
+void Vector3::deserialize(TextInput& t) {
+ t.readSymbol("(");
+ x = (float)t.readNumber();
+ t.readSymbol(",");
+ y = (float)t.readNumber();
+ t.readSymbol(",");
+ z = (float)t.readNumber();
+ t.readSymbol(")");
+}
+
+
+void Vector3::serialize(TextOutput& t) const {
+ t.writeSymbol("(");
+ t.writeNumber(x);
+ t.writeSymbol(",");
+ t.writeNumber(y);
+ t.writeSymbol(",");
+ t.writeNumber(z);
+ t.writeSymbol(")");
+}
+
+
+void Vector3::serialize(BinaryOutput& b) const {
+ b.writeFloat32(x);
+ b.writeFloat32(y);
+ b.writeFloat32(z);
+}
+
+
+Vector3 Vector3::random(Random& r) {
+ Vector3 result;
+ r.sphere(result.x, result.y, result.z);
+ return result;
+}
+
+
+float Vector3::unitize(float fTolerance) {
+ float fMagnitude = magnitude();
+
+ if (fMagnitude > fTolerance) {
+ float fInvMagnitude = 1.0f / fMagnitude;
+ x *= fInvMagnitude;
+ y *= fInvMagnitude;
+ z *= fInvMagnitude;
+ } else {
+ fMagnitude = 0.0f;
+ }
+
+ return fMagnitude;
+}
+
+
+Vector3 Vector3::reflectAbout(const Vector3& normal) const {
+ Vector3 out;
+
+ Vector3 N = normal.direction();
+
+ // 2 * normal.dot(this) * normal - this
+ return N * 2 * this->dot(N) - *this;
+}
+
+
+Vector3 Vector3::cosHemiRandom(const Vector3& normal, Random& r) {
+ debugAssertM(G3D::fuzzyEq(normal.length(), 1.0f),
+ "cosHemiRandom requires its argument to have unit length");
+
+ float x, y, z;
+ r.cosHemi(x, y, z);
+
+ // Make a coordinate system
+ const Vector3& Z = normal;
+
+ Vector3 X, Y;
+ normal.getTangents(X, Y);
+
+ return
+ x * X +
+ y * Y +
+ z * Z;
+}
+
+
+Vector3 Vector3::cosPowHemiRandom(const Vector3& normal, const float k, Random& r) {
+ debugAssertM(G3D::fuzzyEq(normal.length(), 1.0f),
+ "cosPowHemiRandom requires its argument to have unit length");
+
+ float x, y, z;
+ r.cosPowHemi(k, x, y, z);
+
+ // Make a coordinate system
+ const Vector3& Z = normal;
+
+ Vector3 X, Y;
+ normal.getTangents(X, Y);
+
+ return
+ x * X +
+ y * Y +
+ z * Z;
+}
+
+
+Vector3 Vector3::hemiRandom(const Vector3& normal, Random& r) {
+ const Vector3& V = Vector3::random(r);
+
+ if (V.dot(normal) < 0) {
+ return -V;
+ } else {
+ return V;
+ }
+}
+
+//----------------------------------------------------------------------------
+
+Vector3 Vector3::reflectionDirection(const Vector3& normal) const {
+ return -reflectAbout(normal).direction();
+}
+
+//----------------------------------------------------------------------------
+
+Vector3 Vector3::refractionDirection(
+ const Vector3& normal,
+ float iInside,
+ float iOutside) const {
+
+ // From pg. 24 of Henrik Wann Jensen. Realistic Image Synthesis
+ // Using Photon Mapping. AK Peters. ISBN: 1568811470. July 2001.
+
+ // Invert the directions from Wann Jensen's formulation
+ // and normalize the vectors.
+ const Vector3 W = -direction();
+ Vector3 N = normal.direction();
+
+ float h1 = iOutside;
+ float h2 = iInside;
+
+ if (normal.dot(*this) > 0.0f) {
+ h1 = iInside;
+ h2 = iOutside;
+ N = -N;
+ }
+
+ const float hRatio = h1 / h2;
+ const float WdotN = W.dot(N);
+
+ float det = 1.0f - (float)square(hRatio) * (1.0f - (float)square(WdotN));
+
+ if (det < 0) {
+ // Total internal reflection
+ return Vector3::zero();
+ } else {
+ return -hRatio * (W - WdotN * N) - N * sqrt(det);
+ }
+}
+
+//----------------------------------------------------------------------------
+void Vector3::orthonormalize (Vector3 akVector[3]) {
+ // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
+ // orthonormalization produces vectors u0, u1, and u2 as follows,
+ //
+ // u0 = v0/|v0|
+ // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
+ // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
+ //
+ // where |A| indicates length of vector A and A*B indicates dot
+ // product of vectors A and B.
+
+ // compute u0
+ akVector[0].unitize();
+
+ // compute u1
+ float fDot0 = akVector[0].dot(akVector[1]);
+ akVector[1] -= akVector[0] * fDot0;
+ akVector[1].unitize();
+
+ // compute u2
+ float fDot1 = akVector[1].dot(akVector[2]);
+ fDot0 = akVector[0].dot(akVector[2]);
+ akVector[2] -= akVector[0] * fDot0 + akVector[1] * fDot1;
+ akVector[2].unitize();
+}
+
+//----------------------------------------------------------------------------
+void Vector3::generateOrthonormalBasis (Vector3& rkU, Vector3& rkV,
+ Vector3& rkW, bool bUnitLengthW) {
+ if ( !bUnitLengthW )
+ rkW.unitize();
+
+ if ( G3D::abs(rkW.x) >= G3D::abs(rkW.y)
+ && G3D::abs(rkW.x) >= G3D::abs(rkW.z) ) {
+ rkU.x = -rkW.y;
+ rkU.y = + rkW.x;
+ rkU.z = 0.0;
+ } else {
+ rkU.x = 0.0;
+ rkU.y = + rkW.z;
+ rkU.z = -rkW.y;
+ }
+
+ rkU.unitize();
+ rkV = rkW.cross(rkU);
+}
+
+//----------------------------------------------------------------------------
+
+std::string Vector3::toString() const {
+ return G3D::format("(%g, %g, %g)", x, y, z);
+}
+
+
+//----------------------------------------------------------------------------
+
+Matrix3 Vector3::cross() const {
+ return Matrix3( 0, -z, y,
+ z, 0, -x,
+ -y, x, 0);
+}
+
+
+void serialize(const Vector3::Axis& a, class BinaryOutput& bo) {
+ bo.writeUInt8((uint8)a);
+}
+
+void deserialize(Vector3::Axis& a, class BinaryInput& bi) {
+ a = (Vector3::Axis)bi.readUInt8();
+}
+
+//----------------------------------------------------------------------------
+// 2-char swizzles
+
+Vector2 Vector3::xx() const { return Vector2 (x, x); }
+Vector2 Vector3::yx() const { return Vector2 (y, x); }
+Vector2 Vector3::zx() const { return Vector2 (z, x); }
+Vector2 Vector3::xy() const { return Vector2 (x, y); }
+Vector2 Vector3::yy() const { return Vector2 (y, y); }
+Vector2 Vector3::zy() const { return Vector2 (z, y); }
+Vector2 Vector3::xz() const { return Vector2 (x, z); }
+Vector2 Vector3::yz() const { return Vector2 (y, z); }
+Vector2 Vector3::zz() const { return Vector2 (z, z); }
+
+// 3-char swizzles
+
+Vector3 Vector3::xxx() const { return Vector3 (x, x, x); }
+Vector3 Vector3::yxx() const { return Vector3 (y, x, x); }
+Vector3 Vector3::zxx() const { return Vector3 (z, x, x); }
+Vector3 Vector3::xyx() const { return Vector3 (x, y, x); }
+Vector3 Vector3::yyx() const { return Vector3 (y, y, x); }
+Vector3 Vector3::zyx() const { return Vector3 (z, y, x); }
+Vector3 Vector3::xzx() const { return Vector3 (x, z, x); }
+Vector3 Vector3::yzx() const { return Vector3 (y, z, x); }
+Vector3 Vector3::zzx() const { return Vector3 (z, z, x); }
+Vector3 Vector3::xxy() const { return Vector3 (x, x, y); }
+Vector3 Vector3::yxy() const { return Vector3 (y, x, y); }
+Vector3 Vector3::zxy() const { return Vector3 (z, x, y); }
+Vector3 Vector3::xyy() const { return Vector3 (x, y, y); }
+Vector3 Vector3::yyy() const { return Vector3 (y, y, y); }
+Vector3 Vector3::zyy() const { return Vector3 (z, y, y); }
+Vector3 Vector3::xzy() const { return Vector3 (x, z, y); }
+Vector3 Vector3::yzy() const { return Vector3 (y, z, y); }
+Vector3 Vector3::zzy() const { return Vector3 (z, z, y); }
+Vector3 Vector3::xxz() const { return Vector3 (x, x, z); }
+Vector3 Vector3::yxz() const { return Vector3 (y, x, z); }
+Vector3 Vector3::zxz() const { return Vector3 (z, x, z); }
+Vector3 Vector3::xyz() const { return Vector3 (x, y, z); }
+Vector3 Vector3::yyz() const { return Vector3 (y, y, z); }
+Vector3 Vector3::zyz() const { return Vector3 (z, y, z); }
+Vector3 Vector3::xzz() const { return Vector3 (x, z, z); }
+Vector3 Vector3::yzz() const { return Vector3 (y, z, z); }
+Vector3 Vector3::zzz() const { return Vector3 (z, z, z); }
+
+// 4-char swizzles
+
+Vector4 Vector3::xxxx() const { return Vector4 (x, x, x, x); }
+Vector4 Vector3::yxxx() const { return Vector4 (y, x, x, x); }
+Vector4 Vector3::zxxx() const { return Vector4 (z, x, x, x); }
+Vector4 Vector3::xyxx() const { return Vector4 (x, y, x, x); }
+Vector4 Vector3::yyxx() const { return Vector4 (y, y, x, x); }
+Vector4 Vector3::zyxx() const { return Vector4 (z, y, x, x); }
+Vector4 Vector3::xzxx() const { return Vector4 (x, z, x, x); }
+Vector4 Vector3::yzxx() const { return Vector4 (y, z, x, x); }
+Vector4 Vector3::zzxx() const { return Vector4 (z, z, x, x); }
+Vector4 Vector3::xxyx() const { return Vector4 (x, x, y, x); }
+Vector4 Vector3::yxyx() const { return Vector4 (y, x, y, x); }
+Vector4 Vector3::zxyx() const { return Vector4 (z, x, y, x); }
+Vector4 Vector3::xyyx() const { return Vector4 (x, y, y, x); }
+Vector4 Vector3::yyyx() const { return Vector4 (y, y, y, x); }
+Vector4 Vector3::zyyx() const { return Vector4 (z, y, y, x); }
+Vector4 Vector3::xzyx() const { return Vector4 (x, z, y, x); }
+Vector4 Vector3::yzyx() const { return Vector4 (y, z, y, x); }
+Vector4 Vector3::zzyx() const { return Vector4 (z, z, y, x); }
+Vector4 Vector3::xxzx() const { return Vector4 (x, x, z, x); }
+Vector4 Vector3::yxzx() const { return Vector4 (y, x, z, x); }
+Vector4 Vector3::zxzx() const { return Vector4 (z, x, z, x); }
+Vector4 Vector3::xyzx() const { return Vector4 (x, y, z, x); }
+Vector4 Vector3::yyzx() const { return Vector4 (y, y, z, x); }
+Vector4 Vector3::zyzx() const { return Vector4 (z, y, z, x); }
+Vector4 Vector3::xzzx() const { return Vector4 (x, z, z, x); }
+Vector4 Vector3::yzzx() const { return Vector4 (y, z, z, x); }
+Vector4 Vector3::zzzx() const { return Vector4 (z, z, z, x); }
+Vector4 Vector3::xxxy() const { return Vector4 (x, x, x, y); }
+Vector4 Vector3::yxxy() const { return Vector4 (y, x, x, y); }
+Vector4 Vector3::zxxy() const { return Vector4 (z, x, x, y); }
+Vector4 Vector3::xyxy() const { return Vector4 (x, y, x, y); }
+Vector4 Vector3::yyxy() const { return Vector4 (y, y, x, y); }
+Vector4 Vector3::zyxy() const { return Vector4 (z, y, x, y); }
+Vector4 Vector3::xzxy() const { return Vector4 (x, z, x, y); }
+Vector4 Vector3::yzxy() const { return Vector4 (y, z, x, y); }
+Vector4 Vector3::zzxy() const { return Vector4 (z, z, x, y); }
+Vector4 Vector3::xxyy() const { return Vector4 (x, x, y, y); }
+Vector4 Vector3::yxyy() const { return Vector4 (y, x, y, y); }
+Vector4 Vector3::zxyy() const { return Vector4 (z, x, y, y); }
+Vector4 Vector3::xyyy() const { return Vector4 (x, y, y, y); }
+Vector4 Vector3::yyyy() const { return Vector4 (y, y, y, y); }
+Vector4 Vector3::zyyy() const { return Vector4 (z, y, y, y); }
+Vector4 Vector3::xzyy() const { return Vector4 (x, z, y, y); }
+Vector4 Vector3::yzyy() const { return Vector4 (y, z, y, y); }
+Vector4 Vector3::zzyy() const { return Vector4 (z, z, y, y); }
+Vector4 Vector3::xxzy() const { return Vector4 (x, x, z, y); }
+Vector4 Vector3::yxzy() const { return Vector4 (y, x, z, y); }
+Vector4 Vector3::zxzy() const { return Vector4 (z, x, z, y); }
+Vector4 Vector3::xyzy() const { return Vector4 (x, y, z, y); }
+Vector4 Vector3::yyzy() const { return Vector4 (y, y, z, y); }
+Vector4 Vector3::zyzy() const { return Vector4 (z, y, z, y); }
+Vector4 Vector3::xzzy() const { return Vector4 (x, z, z, y); }
+Vector4 Vector3::yzzy() const { return Vector4 (y, z, z, y); }
+Vector4 Vector3::zzzy() const { return Vector4 (z, z, z, y); }
+Vector4 Vector3::xxxz() const { return Vector4 (x, x, x, z); }
+Vector4 Vector3::yxxz() const { return Vector4 (y, x, x, z); }
+Vector4 Vector3::zxxz() const { return Vector4 (z, x, x, z); }
+Vector4 Vector3::xyxz() const { return Vector4 (x, y, x, z); }
+Vector4 Vector3::yyxz() const { return Vector4 (y, y, x, z); }
+Vector4 Vector3::zyxz() const { return Vector4 (z, y, x, z); }
+Vector4 Vector3::xzxz() const { return Vector4 (x, z, x, z); }
+Vector4 Vector3::yzxz() const { return Vector4 (y, z, x, z); }
+Vector4 Vector3::zzxz() const { return Vector4 (z, z, x, z); }
+Vector4 Vector3::xxyz() const { return Vector4 (x, x, y, z); }
+Vector4 Vector3::yxyz() const { return Vector4 (y, x, y, z); }
+Vector4 Vector3::zxyz() const { return Vector4 (z, x, y, z); }
+Vector4 Vector3::xyyz() const { return Vector4 (x, y, y, z); }
+Vector4 Vector3::yyyz() const { return Vector4 (y, y, y, z); }
+Vector4 Vector3::zyyz() const { return Vector4 (z, y, y, z); }
+Vector4 Vector3::xzyz() const { return Vector4 (x, z, y, z); }
+Vector4 Vector3::yzyz() const { return Vector4 (y, z, y, z); }
+Vector4 Vector3::zzyz() const { return Vector4 (z, z, y, z); }
+Vector4 Vector3::xxzz() const { return Vector4 (x, x, z, z); }
+Vector4 Vector3::yxzz() const { return Vector4 (y, x, z, z); }
+Vector4 Vector3::zxzz() const { return Vector4 (z, x, z, z); }
+Vector4 Vector3::xyzz() const { return Vector4 (x, y, z, z); }
+Vector4 Vector3::yyzz() const { return Vector4 (y, y, z, z); }
+Vector4 Vector3::zyzz() const { return Vector4 (z, y, z, z); }
+Vector4 Vector3::xzzz() const { return Vector4 (x, z, z, z); }
+Vector4 Vector3::yzzz() const { return Vector4 (y, z, z, z); }
+Vector4 Vector3::zzzz() const { return Vector4 (z, z, z, z); }
+
+
+
+
+
+
+} // namespace