Come in C++11 and the common issue of dealing with the vector types. These include position (we have the CGPoint in iOS, skVector3 in SpriteKit, and so forth), size (CGSize), colour (4 either floats or bytes), etc.
What changes between these? The number of elements, the type of the elements.
What remains constant? The operations. Dot product can be used for luminance as it can be used for getting the angle between two vectors. Even it can be treated as an innate part of matrix multiplication which we use for general transforms in space, such as from RGB to YUV.
In C++11 we can define something very nice, a template with two parameters, a type and a size. A colour will typically be 3 or 4 components with either a uint8_t or a float as a type. A position can be 2-4 components and is typically a float but can also be a double.
For the constructor, we can use variadic templates to ensure that 0-N components can be initialized at once. For example, in a RGBA colour we could initialize just the first 3 components.
Pushing this idea further, we can make a lot of code much simpler. Consider parsing a range of memory containing an image. We usually have a stride for the x and y which determines how many bytes until the next x pixel and next y pixel. X is typically 4 for 32-bit colour and Y is the width of the image times 4.
Imagine we were to store the strides in a vector, then we could dot the stride with the desired pixel position to get the byte offset. We then have replaced what may appear to be a bunch of semi-random operations all over the code with dot products.
Yes, the example is contrived, and would need some tweaking to be just as efficient - however the point is that all the varied structures described above can be represented using a single structure with a common set of operations.
Consider, my vector for a colour is now defined as: typedef Vector<uint8_t, 4> Colour;
For small hobbyist projects, this is an essential trick to have a rich set of types with relatively little effort.
Update March 1st, 2015 -- Sample code:
Update March 1st, 2015 -- Sample code:
#pragma once//
#include <assert.h>
#include <cmath>
#include <initializer_list>
#include <stdlib.h>
template<class T, int N>
class LVector
{
private:
typedef LVector<T, N> _type;
T _d[N];
// Utility so constructor can take N elements
LVector(T*, int) {}
template<typename ... Args>
LVector(T *idx, T v, Args... args)
: LVector(idx+1, args...)
{
assert(idx <= _d);
idx[0] = v;
}
// Utility so swizzle can take N elements
template<int M>
void _swizzle(LVector<T, M> &ref, const int i)
{ assert(i == M); /* Ensure that we have given all params. */ }
template<int M, typename ... Args>
void _swizzle(LVector<T, M> &ref, const int i, const int idx, Args... args)
{
ref._d[i] = (*this)[idx];
_swizzle(ref, i+1, args...);
}
public:
LVector() = default;
LVector(const LVector<T, N>&) = default;
template<typename ... Args>
LVector(T v, Args... args)
: LVector(_d+1, args...)
{
static_assert(N > 0, "Too many elements for size of vector");
_d[0] = v;
}
_type operator+(const _type &a) const
{
_type r;
for (int i=0; i<N; i++)
r._d[i] = _d[i] + a._d[i];
return r;
}
// Swizzle is a common operation to extract vectors.
template<int M, typename ... Args>
LVector<T, M> swizzle(Args... args)
{
LVector<T, M> v;
_swizzle(v, args...);
return v;
}
// Cast to bool (enables operators to work)
operator bool() const
{
for (int i=0; i<N; i++)
{ if (_d[i] != 0) return false; }
return false;
}
// Comparators (we return masks as they may be multiplied + avoid type issues)
_type operator >(const T& a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] > a) ? 1 : 0; }
return r;
}
_type operator >=(const T& a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] >= a) ? 1 : 0; }
return r;
}
_type operator >(const _type &a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] > a._d[i]) ? 1 : 0; }
return r;
}
_type operator <(const T& a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] < a) ? 1 : 0; }
return r;
}
_type operator <(const _type &a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] < a._d[i]) ? 1 : 0; }
return r;
}
_type operator ==(const _type &a) const
{
_type r;
for (int i=0; i<N; i++)
{ r._d[i] = (_d[i] == a._d[i]) ? 1 : 0; }
return r;
}
// Easy indexing
T &operator[](int i) { return _d[i]; }
T operator[](int i) const { return _d[i]; }
// C++11 utilities
static int size() { return N; }
T* begin() { return _d; }
T* end() { return _d+N; }
};
// Useful derived types
typedef LVector<uint8_t, 4> LColour;
typedef LVector<float, 2> LVector2;
typedef LVector<float, 3> LVector3;
typedef LVector<int, 3> LIVector3;
// Common offsets
enum
{
kX = 0,
kY = 1,
kZ = 2,
kW = 3,
kR = 0,
kG = 1,
kB = 2,
kA = 3
};
// Useful derived operations
template<class T, int N>
T abs(const LVector<T, N> &v)
{
T s;
for (int i=0; i<N; i++)
s[i] = abs(v[i]);
return s;
}
template<class T, int N>
T dot(const LVector<T, N> &l, const LVector<T, N> &r)
{
T s;
for (int i=0; i<N; i++)
s += l[i] * r[i];
return s;
}
template<class T, int N>
T max(const LVector<T, N> &l)
{
T s = l[0];
for (int i=1; i<N; i++)
{
if (s < l[i])
s = l[i];
}
return s;
}
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