Core/VectorMath.h

   1 //
   2 // Copyright (c) Microsoft. All rights reserved.
   3 // This code is licensed under the MIT License (MIT).
   4 // THIS CODE IS PROVIDED *AS IS* WITHOUT WARRANTY OF
   5 // ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING ANY
   6 // IMPLIED WARRANTIES OF FITNESS FOR A PARTICULAR
   7 // PURPOSE, MERCHANTABILITY, OR NON-INFRINGEMENT.
   8 //
   9 // Developed by Minigraph
  10 //
  11 // Author:  James Stanard
  12 //
  13 // This is a system of classes that wrap DirectXMath in a more object-oriented and concise (readable) way.  While these
  14 // classes are not designed to maximize throughput on the instruction level, they are designed to be easily understood.
  15 // I believe that the source of most math library inefficiency is in their being too confusing and not making the preferred
  16 // way of doing things obvious.  This leaves programmers constantly finding usage patterns that "work for them" but are
  17 // ultimately inefficient and don't use the API the "way it was intended".  The goal of this wrapper is to be cogent and
  18 // familiar.
  19 //
  20 // Note that DirectXMath treats vectors like [1x4] matrices (rows) rather than [4x1] matrices (columns).  Likewise, it
  21 // treats matrices like they are transposed, so that you would multiply a vector and a matrix like so:
  22 //
  23 //    Vector [1x4] = Vector [1x4] * Matrix [4x4]
  24 //
  25 // Applying multiple transforms to a vector involves concatenating on the outside, or right of the previous transform:
  26 //
  27 //    ProjectedPosition = ModelPosition * ModelToWorld * WorldToView * ViewToProj
  28 //
  29 // This is *not* how this API works because it is needlessly contrary to Math textbooks.  It's not "wrong", per se,
  30 // but it's a paradigm I'd like to see changed.  A vector is four floats.  A matrix is four consecutive vectors.  Whether
  31 // you think of them as row or column vectors of a matrix is just a matter of perspective.  In this library, you will see:
  32 //
  33 //    Vector [4x1] = Matrix4 [4x4] * Vector [4x1]
  34 //
  35 // and
  36 //
  37 //    ProjectedPosition = ViewToProj * WorldToView * ModelToWorld * ModelPosition
  38 //
  39 // One very happy result of this is that you can stop transposing every matrix you set in a shader constant buffer.  They
  40 // were always in the right format, you were just multiplying them backwards.  In the shader you should have been calling
  41 // mul( matrix, vector ) rather than mul( vector, matrix ).  Then you wouldn't have needed to transpose the matrix.
  42 //
  43 // It's possible to work in a transposed space:  (B*A*x)ᵀ = xᵀ*Aᵀ*Bᵀ   but why would you want to?
  44 //
  45 // Oh, and we use right-handed coordinate systems because that's what you learned in your Linear Algebra, Calculus, and
  46 // Physics classes.
  47 //
  48 // Peace,
  49 //   James
  50
  51
  52 #pragma once
  53
  54 #include "Math/Scalar.h"
  55 #include "Math/Vector.h"
  56 #include "Math/Quaternion.h"
  57 #include "Math/Matrix3.h"
  58 #include "Math/Transform.h"
  59 #include "Math/Matrix4.h"
  60 #include "Math/Functions.inl"