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mathtool.h
1 // © Copyright 2010 - 2014 BlackTopp Studios Inc.
2 /* This file is part of The Mezzanine Engine.
3 
4  The Mezzanine Engine is free software: you can redistribute it and/or modify
5  it under the terms of the GNU General Public License as published by
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18  'Docs' folder. See 'gpl.txt'
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33  These and other limitations could cause serious legal problems if you ignore
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37  Joseph Toppi - toppij@gmail.com
38  John Blackwood - makoenergy02@gmail.com
39 */
40 #ifndef _mathtool_h
41 #define _mathtool_h
42 
43 #include "vector3.h"
44 
45 namespace Mezzanine
46 {
47  class AxisAlignedBox;
48  class Plane;
49  class Ray;
50  class Sphere;
51  /// @namespace Mezzanine::MathTools
52  /// @brief This namespace is the home of a number of utility variables and methods to facilitate various math related tasks.
53  namespace MathTools
54  {
55  /// @brief This is a type used for the ray intersection tests performed on Planes.
56  /// @details This type provides more verbose return data that can be used for further tests.
57  typedef std::pair<Boolean,Vector3> PlaneRayTestResult;
58  /// @brief This is a type used for the return of a ray intersection test.
59  /// @details This type provides more verbose return data that can be used for further tests.
60  typedef std::pair<Boolean,Ray> GeometryRayTestResult;
61 
62  ///////////////////////////////////////////////////////////////////////////////
63  // Predefined Constants
64 
65  /// @brief Gets Pi.
66  Real MEZZ_LIB GetPi();
67  /// @brief Gets Pi times two.
68  Real MEZZ_LIB GetTwoPi();
69  /// @brief Gets half of Pi.
70  Real MEZZ_LIB GetHalfPi();
71  /// @brief Gets Quarter Pi.
72  Real MEZZ_LIB GetQuarterPi();
73 
74  /// @brief Gets a multiplier used in converting Radian angular units to degrees.
75  Real MEZZ_LIB GetRadToDegMultiplier();
76  /// @brief Gets a multiplier used in converting Degree angular units to Radians.
77  Real MEZZ_LIB GetDegToRadMultiplier();
78 
79  ///////////////////////////////////////////////////////////////////////////////
80  // Real Math & Check Functions
81 
82  /// @brief Rounds a Real up.
83  /// @param Val The value to be rounded.
84  /// @return Returns the result of the rounding.
85  Real MEZZ_LIB Ceil(const Real& Val);
86  /// @brief Rounds a Real down.
87  /// @param Val The value to be rounded.
88  /// @return Returns the result of the rounding.
89  Real MEZZ_LIB Floor(const Real& Val);
90  /// @brief Raises a Real to a power.
91  /// @param Val The base number to be raised.
92  /// @param Power The power (or exponent) to raise the Real by.
93  /// @return Returns the Raised Eeal.
94  Real MEZZ_LIB Pow(const Real& Val, const Real& Power);
95  /// @brief Gets the square root of a Real.
96  /// @param Val The number to be calculated.
97  /// @return Returns the calculated square root.
98  Real MEZZ_LIB Sqrt(const Real& Val);
99  /// @brief Gets the absolute value of a Real.
100  /// @param Val The value to get the absolute value of.
101  /// @return Returns the absolute value of the Real.
102  Real MEZZ_LIB Fabs(const Real& Val);
103  /// @brief Modulo, fo' Reals. Returns the remainder of the division between two Reals.
104  /// @param Numerator The number on top.
105  /// @param Denominator The number on bottom.
106  /// @return Returns the remainder of division between the two Reals passed in.
107  Real MEZZ_LIB Fmod(const Real& Numerator, const Real& Denominator);
108  /// @brief Checks to see if two Reals are within a certain range of each other.
109  /// @param First The first of two Reals to compare.
110  /// @param Second The second of two Reals to compare.
111  /// @param Tolerance The leeway allowed in how far the two can be apart.
112  /// @return Returns true if the two numbers are within the amount specified by Tolerance of each other, false otherwise.
113  bool MEZZ_LIB WithinTolerance(const Real& First, const Real& Second, const Real& Tolerance);
114 
115  ///////////////////////////////////////////////////////////////////////////////
116  // Angle Calculation Functions and Values
117 
118  /// @brief Calculates the Cosine of an angle.
119  /// @param Radians The angle to be computed in Radians.
120  /// @return Returns a Real representing the Cosine of the angle provided.
121  Real MEZZ_LIB Cos(const Real& Radians);
122  /// @brief Calculates the Sine of an angle.
123  /// @param Radians The angle to be computed in Radians.
124  /// @return Returns a Real representing the Sine of the angle provided.
125  Real MEZZ_LIB Sin(const Real& Radians);
126  /// @brief Calculates the Tangent of an angle.
127  /// @param Radians The angle to be computed in Radians.
128  /// @return Returns a Real representing the Tangent of the angle provided.
129  Real MEZZ_LIB Tan(const Real& Radians);
130  /// @brief Calculates the principal value of the arc Cosine of an angle.
131  /// @param Interval The Interval to calculate the arc Cosine. Range is -1.0 to 1.0.
132  /// @return Returns a Real representing the principal value of the arc Cosine of the angle provided in Radians.
133  Real MEZZ_LIB ACos(const Real& Interval);
134  /// @brief Calculates the principal value of the arc Sine of an angle.
135  /// @param Interval The Interval to calculate the arc Cosine. Range is -1.0 to 1.0.
136  /// @return Returns a Real representing the principal value of the arc Sine of the angle provided in Radians.
137  Real MEZZ_LIB ASin(const Real& Interval);
138  /// @brief Calculates the principal value of the arc Tangent of an angle.
139  /// @param Interval The Interval to calculate the arc Cosine. Range is -1.0 to 1.0.
140  /// @return Returns a Real representing the principal value of the arc Tangent of the angle provided in Radians.
141  Real MEZZ_LIB ATan(const Real& Interval);
142 
143  ///////////////////////////////////////////////////////////////////////////////
144  // Angle Conversion Functions and Values
145 
146  /// @brief Converts an angle in Degree's to the same angle Radians.
147  /// @param Degrees The number of Degree's to convert.
148  /// @return Returns the converted number in Radians.
149  Real MEZZ_LIB DegreesToRadians(const Real& Degrees);
150  /// @brief Converts an angle in Radians's to the same angle Degrees.
151  /// @param Radians The number of Radians's to convert.
152  /// @return Returns the converted number in Degrees.
153  Real MEZZ_LIB RadiansToDegrees(const Real& Radians);
154 
155  ///////////////////////////////////////////////////////////////////////////////
156  // Geometry Math
157 
158  ///////////////////////////////////////////////////////////////////////////////
159  // Geometry Intersection Query
160 
161  /// @brief Checks to see if a point in 3D space is within an AABB.
162  /// @param Box The AABB to check if the point is inside.
163  /// @param Point The point in 3D space to check if it is within the AABB.
164  /// @return Returns true if the provided point is within the AABB, false otherwise.
165  Boolean MEZZ_LIB IsInside(const AxisAlignedBox& Box, const Vector3& Point);
166  /// @brief Checks to see if a point in 3D space is within a Sphere.
167  /// @param Ball The Sphere to check if the point is inside.
168  /// @param Point The point in 3D space to check if it is within the Sphere.
169  /// @return Returns true if the provided point is within the sphere, false otherwise.
170  Boolean MEZZ_LIB IsInside(const Sphere& Ball, const Vector3& Point);
171 
172  /// @brief Checks to see if an AABB and Sphere are overlapping.
173  /// @param Box The AABB to check for overlap.
174  /// @param Ball The Sphere to check for overlap.
175  /// @return Returns true if the AABB and Sphere overlap, false otherwise.
176  Boolean MEZZ_LIB Overlap(const AxisAlignedBox& Box, const Sphere& Ball);
177  /// @brief Checks to see if an AANN and Plane are overlapping.
178  /// @param Box The AABB to check for overlap.
179  /// @param Surface The Plane to check for overlap.
180  /// @return Returns true if the AABB and Pland overlap, false otherwise.
181  Boolean MEZZ_LIB Overlap(const AxisAlignedBox& Box, const Plane& Surface);
182  /// @brief Checks to see if a Plane and Sphere are overlapping.
183  /// @param Surface The Plane to check for overlap.
184  /// @param Ball The Sphere to check for overlap.
185  /// @return Returns true if the Plane and Sphere overlap, false otherwise.
186  Boolean MEZZ_LIB Overlap(const Plane& Surface, const Sphere& Ball);
187 
188  /// @brief Checks to see if two AABBs are overlapping.
189  /// @param Box1 The first AABB to check for overlap.
190  /// @param Box2 The second AABB to check for overlap.
191  /// @return Returns true if the two AABBs are overlapping, false otherwise.
192  Boolean MEZZ_LIB Overlap(const AxisAlignedBox& Box1, const AxisAlignedBox& Box2);
193  /// @brief Checks to see if two Spheres are overlapping.
194  /// @param Ball1 The first Sphere to check for overlap.
195  /// @param Ball2 The second Sphere to check for overlap.
196  /// @return Returns true if the two Spheres are overlapping, false otherwise.
197  Boolean MEZZ_LIB Overlap(const Sphere& Ball1, const Sphere& Ball2);
198  /// @brief Checks to see if two Planes are overlapping.
199  /// @param Surface1 The first Plane to check for overlap.
200  /// @param Surface2 The second Plane to check for overlap.
201  /// @return Returns true if the two Planes are overlapping, false otherwise.
202  Boolean MEZZ_LIB Overlap(const Plane& Surface1, const Plane& Surface2);
203 
204  /// @brief Checks to see if a ray intersects with a Plane.
205  /// @param Surface The Plane to check for intersection.
206  /// @param Cast The casted ray to check for intersection.
207  /// @return Returns true if the ray intersects with the provided Plane.
208  PlaneRayTestResult MEZZ_LIB Intersects(const Plane& Surface, const Ray& Cast);
209  /// @brief Checks to see if a ray intersects with an AABB.
210  /// @param Box The AABB to check for intersection.
211  /// @param Cast The casted ray to check for intersection.
212  /// @return Returns a std::pair containing whether or not the ray hit, and if it did also a ray that is the subsection of the casted ray that went through the AABB.
213  GeometryRayTestResult MEZZ_LIB Intersects(const AxisAlignedBox& Box, const Ray& Cast);
214  /// @brief Checks to see if a ray intersects with a Sphere.
215  /// @param Ball The Sphere to check for intersection.
216  /// @param Cast The casted ray to check for intersection.
217  /// @return Returns a std::pair containing whether or not the ray hit, and if it did also a ray that is the subsection of the casted ray that went through the Sphere.
218  GeometryRayTestResult MEZZ_LIB Intersects(const Sphere& Ball, const Ray& Cast);
219  }//MathTools
220 }//Mezzanine
221 
222 #endif
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