diff options
Diffstat (limited to 'indra/llmath/v3dmath.h')
-rw-r--r-- | indra/llmath/v3dmath.h | 378 |
1 files changed, 189 insertions, 189 deletions
diff --git a/indra/llmath/v3dmath.h b/indra/llmath/v3dmath.h index ece8c54ea4..fcce2c30eb 100644 --- a/indra/llmath/v3dmath.h +++ b/indra/llmath/v3dmath.h @@ -32,128 +32,127 @@ class LLVector3d { - public: - F64 mdV[3]; - - const static LLVector3d zero; - const static LLVector3d x_axis; - const static LLVector3d y_axis; - const static LLVector3d z_axis; - const static LLVector3d x_axis_neg; - const static LLVector3d y_axis_neg; - const static LLVector3d z_axis_neg; - - inline LLVector3d(); // Initializes LLVector3d to (0, 0, 0) - inline LLVector3d(const F64 x, const F64 y, const F64 z); // Initializes LLVector3d to (x. y, z) - inline explicit LLVector3d(const F64 *vec); // Initializes LLVector3d to (vec[0]. vec[1], vec[2]) - inline explicit LLVector3d(const LLVector3 &vec); - explicit LLVector3d(const LLSD& sd) - { - setValue(sd); - } - - void setValue(const LLSD& sd) - { - mdV[0] = sd[0].asReal(); - mdV[1] = sd[1].asReal(); - mdV[2] = sd[2].asReal(); - } - - LLSD getValue() const - { - LLSD ret; - ret[0] = mdV[0]; - ret[1] = mdV[1]; - ret[2] = mdV[2]; - return ret; - } - - inline bool isFinite() const; // checks to see if all values of LLVector3d are finite - bool clamp(const F64 min, const F64 max); // Clamps all values to (min,max), returns true if data changed - bool abs(); // sets all values to absolute value of original value (first octant), returns true if changed - - inline const LLVector3d& clear(); // Clears LLVector3d to (0, 0, 0, 1) - inline const LLVector3d& clearVec(); // deprecated - inline const LLVector3d& setZero(); // Zero LLVector3d to (0, 0, 0, 0) - inline const LLVector3d& zeroVec(); // deprecated - inline const LLVector3d& set(const F64 x, const F64 y, const F64 z); // Sets LLVector3d to (x, y, z, 1) - inline const LLVector3d& set(const LLVector3d &vec); // Sets LLVector3d to vec - inline const LLVector3d& set(const F64 *vec); // Sets LLVector3d to vec - inline const LLVector3d& set(const LLVector3 &vec); - inline const LLVector3d& setVec(const F64 x, const F64 y, const F64 z); // deprecated - inline const LLVector3d& setVec(const LLVector3d &vec); // deprecated - inline const LLVector3d& setVec(const F64 *vec); // deprecated - inline const LLVector3d& setVec(const LLVector3 &vec); // deprecated - - F64 magVec() const; // deprecated - F64 magVecSquared() const; // deprecated - inline F64 normVec(); // deprecated - - F64 length() const; // Returns magnitude of LLVector3d - F64 lengthSquared() const; // Returns magnitude squared of LLVector3d - inline F64 normalize(); // Normalizes and returns the magnitude of LLVector3d - - const LLVector3d& rotVec(const F64 angle, const LLVector3d &vec); // Rotates about vec by angle radians - const LLVector3d& rotVec(const F64 angle, const F64 x, const F64 y, const F64 z); // Rotates about x,y,z by angle radians - const LLVector3d& rotVec(const LLMatrix3 &mat); // Rotates by LLMatrix4 mat - const LLVector3d& rotVec(const LLQuaternion &q); // Rotates by LLQuaternion q - - bool isNull() const; // Returns true if vector has a _very_small_ length - bool isExactlyZero() const { return !mdV[VX] && !mdV[VY] && !mdV[VZ]; } - - const LLVector3d& operator=(const LLVector4 &a); - - F64 operator[](int idx) const { return mdV[idx]; } - F64 &operator[](int idx) { return mdV[idx]; } - - friend LLVector3d operator+(const LLVector3d& a, const LLVector3d& b); // Return vector a + b - friend LLVector3d operator-(const LLVector3d& a, const LLVector3d& b); // Return vector a minus b - friend F64 operator*(const LLVector3d& a, const LLVector3d& b); // Return a dot b - friend LLVector3d operator%(const LLVector3d& a, const LLVector3d& b); // Return a cross b - friend LLVector3d operator*(const LLVector3d& a, const F64 k); // Return a times scaler k - friend LLVector3d operator/(const LLVector3d& a, const F64 k); // Return a divided by scaler k - friend LLVector3d operator*(const F64 k, const LLVector3d& a); // Return a times scaler k - friend bool operator==(const LLVector3d& a, const LLVector3d& b); // Return a == b - friend bool operator!=(const LLVector3d& a, const LLVector3d& b); // Return a != b - - friend const LLVector3d& operator+=(LLVector3d& a, const LLVector3d& b); // Return vector a + b - friend const LLVector3d& operator-=(LLVector3d& a, const LLVector3d& b); // Return vector a minus b - friend const LLVector3d& operator%=(LLVector3d& a, const LLVector3d& b); // Return a cross b - friend const LLVector3d& operator*=(LLVector3d& a, const F64 k); // Return a times scaler k - friend const LLVector3d& operator/=(LLVector3d& a, const F64 k); // Return a divided by scaler k - - friend LLVector3d operator-(const LLVector3d& a); // Return vector -a - - friend std::ostream& operator<<(std::ostream& s, const LLVector3d& a); // Stream a - - static bool parseVector3d(const std::string& buf, LLVector3d* value); +public: + F64 mdV[3]; + + const static LLVector3d zero; + const static LLVector3d x_axis; + const static LLVector3d y_axis; + const static LLVector3d z_axis; + const static LLVector3d x_axis_neg; + const static LLVector3d y_axis_neg; + const static LLVector3d z_axis_neg; + + inline LLVector3d(); // Initializes LLVector3d to (0, 0, 0) + inline LLVector3d(const F64 x, const F64 y, const F64 z); // Initializes LLVector3d to (x. y, z) + inline explicit LLVector3d(const F64 *vec); // Initializes LLVector3d to (vec[0]. vec[1], vec[2]) + inline explicit LLVector3d(const LLVector3 &vec); + explicit LLVector3d(const LLSD& sd) + { + setValue(sd); + } + + void setValue(const LLSD& sd) + { + mdV[VX] = sd[0].asReal(); + mdV[VY] = sd[1].asReal(); + mdV[VZ] = sd[2].asReal(); + } + LLSD getValue() const + { + LLSD ret; + ret[0] = mdV[VX]; + ret[1] = mdV[VY]; + ret[2] = mdV[VZ]; + return ret; + } + + inline bool isFinite() const; // checks to see if all values of LLVector3d are finite + bool clamp(const F64 min, const F64 max); // Clamps all values to (min,max), returns true if data changed + bool abs(); // sets all values to absolute value of original value (first octant), returns true if changed + + inline const LLVector3d& clear(); // Clears LLVector3d to (0, 0, 0, 1) + inline const LLVector3d& clearVec(); // deprecated + inline const LLVector3d& setZero(); // Zero LLVector3d to (0, 0, 0, 0) + inline const LLVector3d& zeroVec(); // deprecated + inline const LLVector3d& set(const F64 x, const F64 y, const F64 z); // Sets LLVector3d to (x, y, z, 1) + inline const LLVector3d& set(const LLVector3d &vec); // Sets LLVector3d to vec + inline const LLVector3d& set(const F64 *vec); // Sets LLVector3d to vec + inline const LLVector3d& set(const LLVector3 &vec); + inline const LLVector3d& setVec(const F64 x, const F64 y, const F64 z); // deprecated + inline const LLVector3d& setVec(const LLVector3d &vec); // deprecated + inline const LLVector3d& setVec(const F64 *vec); // deprecated + inline const LLVector3d& setVec(const LLVector3 &vec); // deprecated + + F64 magVec() const; // deprecated + F64 magVecSquared() const; // deprecated + inline F64 normVec(); // deprecated + + F64 length() const; // Returns magnitude of LLVector3d + F64 lengthSquared() const; // Returns magnitude squared of LLVector3d + inline F64 normalize(); // Normalizes and returns the magnitude of LLVector3d + + const LLVector3d& rotVec(const F64 angle, const LLVector3d &vec); // Rotates about vec by angle radians + const LLVector3d& rotVec(const F64 angle, const F64 x, const F64 y, const F64 z); // Rotates about x,y,z by angle radians + const LLVector3d& rotVec(const LLMatrix3 &mat); // Rotates by LLMatrix4 mat + const LLVector3d& rotVec(const LLQuaternion &q); // Rotates by LLQuaternion q + + bool isNull() const; // Returns true if vector has a _very_small_ length + bool isExactlyZero() const { return !mdV[VX] && !mdV[VY] && !mdV[VZ]; } + + const LLVector3d& operator=(const LLVector4 &a); + + F64 operator[](int idx) const { return mdV[idx]; } + F64 &operator[](int idx) { return mdV[idx]; } + + friend LLVector3d operator+(const LLVector3d& a, const LLVector3d& b); // Return vector a + b + friend LLVector3d operator-(const LLVector3d& a, const LLVector3d& b); // Return vector a minus b + friend F64 operator*(const LLVector3d& a, const LLVector3d& b); // Return a dot b + friend LLVector3d operator%(const LLVector3d& a, const LLVector3d& b); // Return a cross b + friend LLVector3d operator*(const LLVector3d& a, const F64 k); // Return a times scaler k + friend LLVector3d operator/(const LLVector3d& a, const F64 k); // Return a divided by scaler k + friend LLVector3d operator*(const F64 k, const LLVector3d& a); // Return a times scaler k + friend bool operator==(const LLVector3d& a, const LLVector3d& b); // Return a == b + friend bool operator!=(const LLVector3d& a, const LLVector3d& b); // Return a != b + + friend const LLVector3d& operator+=(LLVector3d& a, const LLVector3d& b); // Return vector a + b + friend const LLVector3d& operator-=(LLVector3d& a, const LLVector3d& b); // Return vector a minus b + friend const LLVector3d& operator%=(LLVector3d& a, const LLVector3d& b); // Return a cross b + friend const LLVector3d& operator*=(LLVector3d& a, const F64 k); // Return a times scaler k + friend const LLVector3d& operator/=(LLVector3d& a, const F64 k); // Return a divided by scaler k + + friend LLVector3d operator-(const LLVector3d& a); // Return vector -a + + friend std::ostream& operator<<(std::ostream& s, const LLVector3d& a); // Stream a + + static bool parseVector3d(const std::string& buf, LLVector3d* value); }; typedef LLVector3d LLGlobalVec; inline const LLVector3d &LLVector3d::set(const LLVector3 &vec) { - mdV[0] = vec.mV[0]; - mdV[1] = vec.mV[1]; - mdV[2] = vec.mV[2]; + mdV[VX] = vec.mV[VX]; + mdV[VY] = vec.mV[VY]; + mdV[VZ] = vec.mV[VZ]; return *this; } inline const LLVector3d &LLVector3d::setVec(const LLVector3 &vec) { - mdV[0] = vec.mV[0]; - mdV[1] = vec.mV[1]; - mdV[2] = vec.mV[2]; + mdV[VX] = vec.mV[VX]; + mdV[VY] = vec.mV[VY]; + mdV[VZ] = vec.mV[VZ]; return *this; } inline LLVector3d::LLVector3d(void) { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2] = 0.f; + mdV[VX] = 0.f; + mdV[VY] = 0.f; + mdV[VZ] = 0.f; } inline LLVector3d::LLVector3d(const F64 x, const F64 y, const F64 z) @@ -199,33 +198,33 @@ inline bool LLVector3d::isFinite() const inline const LLVector3d& LLVector3d::clear(void) { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2]= 0.f; + mdV[VX] = 0.f; + mdV[VY] = 0.f; + mdV[VZ] = 0.f; return (*this); } inline const LLVector3d& LLVector3d::clearVec(void) { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2]= 0.f; + mdV[VX] = 0.f; + mdV[VY] = 0.f; + mdV[VZ] = 0.f; return (*this); } inline const LLVector3d& LLVector3d::setZero(void) { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2] = 0.f; + mdV[VX] = 0.f; + mdV[VY] = 0.f; + mdV[VZ] = 0.f; return (*this); } inline const LLVector3d& LLVector3d::zeroVec(void) { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2] = 0.f; + mdV[VX] = 0.f; + mdV[VY] = 0.f; + mdV[VZ] = 0.f; return (*this); } @@ -239,17 +238,17 @@ inline const LLVector3d& LLVector3d::set(const F64 x, const F64 y, const F64 inline const LLVector3d& LLVector3d::set(const LLVector3d &vec) { - mdV[0] = vec.mdV[0]; - mdV[1] = vec.mdV[1]; - mdV[2] = vec.mdV[2]; + mdV[VX] = vec.mdV[VX]; + mdV[VY] = vec.mdV[VY]; + mdV[VZ] = vec.mdV[VZ]; return (*this); } inline const LLVector3d& LLVector3d::set(const F64 *vec) { - mdV[0] = vec[0]; - mdV[1] = vec[1]; - mdV[2] = vec[2]; + mdV[VX] = vec[0]; + mdV[VY] = vec[1]; + mdV[VZ] = vec[2]; return (*this); } @@ -261,61 +260,62 @@ inline const LLVector3d& LLVector3d::setVec(const F64 x, const F64 y, const F return (*this); } -inline const LLVector3d& LLVector3d::setVec(const LLVector3d &vec) +inline const LLVector3d& LLVector3d::setVec(const LLVector3d& vec) { - mdV[0] = vec.mdV[0]; - mdV[1] = vec.mdV[1]; - mdV[2] = vec.mdV[2]; + mdV[VX] = vec.mdV[VX]; + mdV[VY] = vec.mdV[VY]; + mdV[VZ] = vec.mdV[VZ]; return (*this); } -inline const LLVector3d& LLVector3d::setVec(const F64 *vec) +inline const LLVector3d& LLVector3d::setVec(const F64* vec) { - mdV[0] = vec[0]; - mdV[1] = vec[1]; - mdV[2] = vec[2]; + mdV[VX] = vec[VX]; + mdV[VY] = vec[VY]; + mdV[VZ] = vec[VZ]; return (*this); } -inline F64 LLVector3d::normVec(void) +inline F64 LLVector3d::normVec() { - F64 mag = (F32) sqrt(mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]); + F64 mag = (F32)sqrt(mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]); // This explicit cast to F32 limits the precision for numerical stability. + // Without it, Unit test "v3dmath_h" fails at "1:angle_between" on macos. F64 oomag; if (mag > FP_MAG_THRESHOLD) { - oomag = 1.f/mag; - mdV[0] *= oomag; - mdV[1] *= oomag; - mdV[2] *= oomag; + oomag = 1.0/mag; + mdV[VX] *= oomag; + mdV[VY] *= oomag; + mdV[VZ] *= oomag; } else { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2] = 0.f; + mdV[VX] = 0.0; + mdV[VY] = 0.0; + mdV[VZ] = 0.0; mag = 0; } return (mag); } -inline F64 LLVector3d::normalize(void) +inline F64 LLVector3d::normalize() { - F64 mag = (F32) sqrt(mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]); + F64 mag = (F32)sqrt(mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]); // Same as in normVec() above. F64 oomag; if (mag > FP_MAG_THRESHOLD) { - oomag = 1.f/mag; - mdV[0] *= oomag; - mdV[1] *= oomag; - mdV[2] *= oomag; + oomag = 1.0/mag; + mdV[VX] *= oomag; + mdV[VY] *= oomag; + mdV[VZ] *= oomag; } else { - mdV[0] = 0.f; - mdV[1] = 0.f; - mdV[2] = 0.f; + mdV[VX] = 0.0; + mdV[VY] = 0.0; + mdV[VZ] = 0.0; mag = 0; } return (mag); @@ -323,24 +323,24 @@ inline F64 LLVector3d::normalize(void) // LLVector3d Magnitude and Normalization Functions -inline F64 LLVector3d::magVec(void) const +inline F64 LLVector3d::magVec() const { - return (F32) sqrt(mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]); + return sqrt(mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]); } -inline F64 LLVector3d::magVecSquared(void) const +inline F64 LLVector3d::magVecSquared() const { - return mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]; + return mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]; } -inline F64 LLVector3d::length(void) const +inline F64 LLVector3d::length() const { - return (F32) sqrt(mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]); + return sqrt(mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]); } -inline F64 LLVector3d::lengthSquared(void) const +inline F64 LLVector3d::lengthSquared() const { - return mdV[0]*mdV[0] + mdV[1]*mdV[1] + mdV[2]*mdV[2]; + return mdV[VX]*mdV[VX] + mdV[VY]*mdV[VY] + mdV[VZ]*mdV[VZ]; } inline LLVector3d operator+(const LLVector3d& a, const LLVector3d& b) @@ -357,109 +357,109 @@ inline LLVector3d operator-(const LLVector3d& a, const LLVector3d& b) inline F64 operator*(const LLVector3d& a, const LLVector3d& b) { - return (a.mdV[0]*b.mdV[0] + a.mdV[1]*b.mdV[1] + a.mdV[2]*b.mdV[2]); + return (a.mdV[VX]*b.mdV[VX] + a.mdV[VY]*b.mdV[VY] + a.mdV[VZ]*b.mdV[VZ]); } inline LLVector3d operator%(const LLVector3d& a, const LLVector3d& b) { - return LLVector3d( a.mdV[1]*b.mdV[2] - b.mdV[1]*a.mdV[2], a.mdV[2]*b.mdV[0] - b.mdV[2]*a.mdV[0], a.mdV[0]*b.mdV[1] - b.mdV[0]*a.mdV[1] ); + return LLVector3d( a.mdV[VY]*b.mdV[VZ] - b.mdV[VY]*a.mdV[VZ], a.mdV[VZ]*b.mdV[VX] - b.mdV[VZ]*a.mdV[VX], a.mdV[VX]*b.mdV[VY] - b.mdV[VX]*a.mdV[VY] ); } inline LLVector3d operator/(const LLVector3d& a, const F64 k) { F64 t = 1.f / k; - return LLVector3d( a.mdV[0] * t, a.mdV[1] * t, a.mdV[2] * t ); + return LLVector3d( a.mdV[VX] * t, a.mdV[VY] * t, a.mdV[VZ] * t ); } inline LLVector3d operator*(const LLVector3d& a, const F64 k) { - return LLVector3d( a.mdV[0] * k, a.mdV[1] * k, a.mdV[2] * k ); + return LLVector3d( a.mdV[VX] * k, a.mdV[VY] * k, a.mdV[VZ] * k ); } inline LLVector3d operator*(F64 k, const LLVector3d& a) { - return LLVector3d( a.mdV[0] * k, a.mdV[1] * k, a.mdV[2] * k ); + return LLVector3d( a.mdV[VX] * k, a.mdV[VY] * k, a.mdV[VZ] * k ); } inline bool operator==(const LLVector3d& a, const LLVector3d& b) { - return ( (a.mdV[0] == b.mdV[0]) - &&(a.mdV[1] == b.mdV[1]) - &&(a.mdV[2] == b.mdV[2])); + return ( (a.mdV[VX] == b.mdV[VX]) + &&(a.mdV[VY] == b.mdV[VY]) + &&(a.mdV[VZ] == b.mdV[VZ])); } inline bool operator!=(const LLVector3d& a, const LLVector3d& b) { - return ( (a.mdV[0] != b.mdV[0]) - ||(a.mdV[1] != b.mdV[1]) - ||(a.mdV[2] != b.mdV[2])); + return ( (a.mdV[VX] != b.mdV[VX]) + ||(a.mdV[VY] != b.mdV[VY]) + ||(a.mdV[VZ] != b.mdV[VZ])); } inline const LLVector3d& operator+=(LLVector3d& a, const LLVector3d& b) { - a.mdV[0] += b.mdV[0]; - a.mdV[1] += b.mdV[1]; - a.mdV[2] += b.mdV[2]; + a.mdV[VX] += b.mdV[VX]; + a.mdV[VY] += b.mdV[VY]; + a.mdV[VZ] += b.mdV[VZ]; return a; } inline const LLVector3d& operator-=(LLVector3d& a, const LLVector3d& b) { - a.mdV[0] -= b.mdV[0]; - a.mdV[1] -= b.mdV[1]; - a.mdV[2] -= b.mdV[2]; + a.mdV[VX] -= b.mdV[VX]; + a.mdV[VY] -= b.mdV[VY]; + a.mdV[VZ] -= b.mdV[VZ]; return a; } inline const LLVector3d& operator%=(LLVector3d& a, const LLVector3d& b) { - LLVector3d ret( a.mdV[1]*b.mdV[2] - b.mdV[1]*a.mdV[2], a.mdV[2]*b.mdV[0] - b.mdV[2]*a.mdV[0], a.mdV[0]*b.mdV[1] - b.mdV[0]*a.mdV[1]); + LLVector3d ret( a.mdV[VY]*b.mdV[VZ] - b.mdV[VY]*a.mdV[VZ], a.mdV[VZ]*b.mdV[VX] - b.mdV[VZ]*a.mdV[VX], a.mdV[VX]*b.mdV[VY] - b.mdV[VX]*a.mdV[VY]); a = ret; return a; } inline const LLVector3d& operator*=(LLVector3d& a, const F64 k) { - a.mdV[0] *= k; - a.mdV[1] *= k; - a.mdV[2] *= k; + a.mdV[VX] *= k; + a.mdV[VY] *= k; + a.mdV[VZ] *= k; return a; } inline const LLVector3d& operator/=(LLVector3d& a, const F64 k) { F64 t = 1.f / k; - a.mdV[0] *= t; - a.mdV[1] *= t; - a.mdV[2] *= t; + a.mdV[VX] *= t; + a.mdV[VY] *= t; + a.mdV[VZ] *= t; return a; } inline LLVector3d operator-(const LLVector3d& a) { - return LLVector3d( -a.mdV[0], -a.mdV[1], -a.mdV[2] ); + return LLVector3d( -a.mdV[VX], -a.mdV[VY], -a.mdV[VZ] ); } inline F64 dist_vec(const LLVector3d& a, const LLVector3d& b) { - F64 x = a.mdV[0] - b.mdV[0]; - F64 y = a.mdV[1] - b.mdV[1]; - F64 z = a.mdV[2] - b.mdV[2]; + F64 x = a.mdV[VX] - b.mdV[VX]; + F64 y = a.mdV[VY] - b.mdV[VY]; + F64 z = a.mdV[VZ] - b.mdV[VZ]; return (F32) sqrt( x*x + y*y + z*z ); } inline F64 dist_vec_squared(const LLVector3d& a, const LLVector3d& b) { - F64 x = a.mdV[0] - b.mdV[0]; - F64 y = a.mdV[1] - b.mdV[1]; - F64 z = a.mdV[2] - b.mdV[2]; + F64 x = a.mdV[VX] - b.mdV[VX]; + F64 y = a.mdV[VY] - b.mdV[VY]; + F64 z = a.mdV[VZ] - b.mdV[VZ]; return x*x + y*y + z*z; } inline F64 dist_vec_squared2D(const LLVector3d& a, const LLVector3d& b) { - F64 x = a.mdV[0] - b.mdV[0]; - F64 y = a.mdV[1] - b.mdV[1]; + F64 x = a.mdV[VX] - b.mdV[VX]; + F64 y = a.mdV[VY] - b.mdV[VY]; return x*x + y*y; } |