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* mathfuncs.h - General mathematic functions header
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* Copyright (C) 2012, D Haley
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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#include "assertion.h"
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#include "endianTest.h"
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//!A 3D point data class storage
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/*! A 3D point data class
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* contains operator overloads and some basic
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* mathematical functions
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//!Constructor with initialising values
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inline Point3D(float x,float y,float z)
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{ value[0] = x, value[1] = y, value[2] = z;}
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//!Set by value (ith dim 0, 1 2)
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inline void setValue(unsigned int ui, float val){value[ui]=val;};
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inline void setValue(float fX,float fY, float fZ)
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{value[0]=fX; value[1]=fY; value[2]=fZ;}
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inline void setValueArr(const float *val)
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//!Get value of ith dim (0, 1, 2)
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inline float getValue(unsigned int ui) const {return value[ui];};
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//Retrieve the internal pointer. Only use if you know why.
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inline const float *getValueArr() const { return value;};
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//!get into an array (note array must hold sizeof(float)*3 bytes of valid mem
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void copyValueArr(float *value) const;
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//!Add a point to this, without generating a return value
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void add(const Point3D &obj);
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bool operator==(const Point3D &pt) const;
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//!assignment operator
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const Point3D &operator=(const Point3D &pt);
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const Point3D &operator+=(const Point3D &pt);
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const Point3D operator+(float f) const;
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//!multiplication operator
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const Point3D &operator*=(const float scale);
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const Point3D operator+(const Point3D &pt) const;
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//!elemental multiplication
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const Point3D operator*(float scale) const;
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const Point3D operator*(const Point3D &pt) const;
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const Point3D operator/(float scale) const;
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const Point3D operator-(const Point3D &pt) const;
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//!returns a negative of the existing value
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const Point3D operator-() const;
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//!Output streaming operator. Users (x,y,z) as format for output
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friend std::ostream &operator<<(std::ostream &stream, const Point3D &);
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//!make point unit magnitude, maintaining direction
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//!returns the square of distance another pt
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float sqrDist(const Point3D &pt) const;
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//!Calculate the dot product of this and another pint
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float dotProd(const Point3D &pt) const;
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//!Calculate the cross product of this and another point
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Point3D crossProd(const Point3D &pt) const;
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//!Calculate the angle between two position vectors in radiians
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float angle(const Point3D &pt) const;
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//!overload for array indexing returns |pt|^2
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float sqrMag() const;
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inline float operator[](unsigned int ui) const { ASSERT(ui < 3); return value[ui];}
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//!Retrieve element by referene
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inline float &operator[](unsigned int ui) { ASSERT(ui < 3); return value[ui];}
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//!Is a given point stored inside a box bounded by orign and this pt?
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/*!returns true if this point is located inside (0,0,0) -> Farpoint
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* assuming box shape (non zero edges return false)
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* farPoint must be positive in all dim
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bool insideBox(const Point3D &farPoint) const;
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//!Tests if this point lies inside the rectangular prism
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/*!Returns true if this point lies inside the box bounded
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* by lowPoint and highPoint
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bool insideBox(const Point3D &lowPoint, const Point3D &highPoint) const;
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//!Makes each value negative of old value
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//Perform a 3x3 matrix transformation.
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void transform3x3(const float *matrix);
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//Perform a cross-product based orthogonalisation
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//with the specified vector
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bool orthogonalise(const Point3D &p);
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#ifdef __LITTLE_ENDIAN__
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//!Flip the endian state for data stored in this point
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//Do NOT use multiple instances of this in your code
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//with the same initialisation technique (e.g. initialising from system clock)
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//this would be BAD, correlations might well be introduced into your results
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//that are simply a result of using correlated random sequences!!! (think about it)
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//use ONE random number generator in the project, initialise it and then "register"
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//it with any objects that need a random generator.
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void initialise(int seedVal);
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float genUniformDev();
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//This generates a number chosen from
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//a gaussian distribution range is (-inf, inf)
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//Uses quaternion mathematics to perform a rotation around your favourite axis
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//IMPORTANT: rotVec must be normalised before passing to this function
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//failure to do so will have weird results
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//Note result is stored in point passed as argument
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//angle is in radians.
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void quat_rot(Point3f *point, Point3f *rotVec, float angle);
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//Retrieve the quaternion for repeated rotations. Pass to the quat_rot_apply_quats.
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//angle is in radians
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void quat_get_rot_quat(Point3f *rotVec, float angle, Quaternion *rotQuat);
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//Use previously generated quats from quat_get_rot_quats to rotate a point
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void quat_rot_apply_quat(Point3f *point, Quaternion *rotQuat);
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//This class implements a Linear Feedback Shift Register (in software)
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//This is a mathematical construct based upon polynomials over closed natural numbers (N mod p).
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//This will generate a weakly random digit string, but with guaranteed no duplicates, using O(1)
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//memory and O(n) calls. The no duplicate guarantee is weak-ish, with no repetition in the
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//shift register for 2^n-1 iterations. n can be set by setMaskPeriod.
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class LinearFeedbackShiftReg
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//Get a value from the shift register, and advance
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//Set the internal lfsr state. Note 0 is the lock-up state.
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void setState(size_t newState) { lfsr=newState;};
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//set the mask to use such that the period is 2^n-1. 3 is minimum 60 is maximum
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void setMaskPeriod(unsigned int newMask);
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//!Check the validity of the table
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//Determines the volume of a quadrilateral pyramid
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//input points "planarpts" must be adjacent (connected) by
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//0 <-> 1 <-> 2 <-> 0, all points connected to apex
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double pyramidVol(const Point3D *planarPts, const Point3D &apex);
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//!Inline func for calculating a(dot)b
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inline float dotProduct(float a1, float a2, float a3,
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float b1, float b2, float b3)
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return a1*b1 + a2*b2 + a3* b3;
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inline unsigned int ilog2(unsigned int value)
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while( (value >> l) > 1 )
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src/mathfuncs.h
