// This code is in the public domain -- castanyo@yahoo.es

#include <nvcore/Containers.h>
#include <nvcore/Ptr.h>

#include <nvmath/Color.h>

#include "FloatImage.h"
#include "Filter.h"
#include "Image.h"

#include <math.h>

using namespace nv;

namespace 
{
	static int round(float f)
	{
		return int(f);
	}

	static float frac(float f)
	{
		return f - floor(f);
	}
}


/// Ctor.
FloatImage::FloatImage() : m_width(0), m_height(0), 
	m_componentNum(0), m_count(0), m_mem(NULL)
{
}

/// Ctor. Init from image.
FloatImage::FloatImage(const Image * img) : m_width(0), m_height(0), 
	m_componentNum(0), m_count(0), m_mem(NULL)
{
	initFrom(img);
}

/// Dtor.
FloatImage::~FloatImage()
{
	free();
}


/// Init the floating point image from a regular image.
void FloatImage::initFrom(const Image * img)
{
	nvCheck(img != NULL);
	
	allocate(4, img->width(), img->height());
	
	float * red_channel = channel(0);
	float * green_channel = channel(1);
	float * blue_channel = channel(2);
	float * alpha_channel = channel(3);
	
	const uint count = m_width * m_height;
	for(uint i = 0; i < count; i++) {
		Color32 pixel = img->pixel(i);
		red_channel[i] = float(pixel.r) / 255.0f;
		green_channel[i] = float(pixel.g) / 255.0f;
		blue_channel[i] = float(pixel.b) / 255.0f;
		alpha_channel[i] = float(pixel.a) / 255.0f;
	}
}

/// Convert the floating point image to a regular image.
Image * FloatImage::createImage(uint base_component/*= 0*/, uint num/*= 4*/) const
{
	nvCheck(num <= 4);
	nvCheck(base_component + num <= m_componentNum);
	
	AutoPtr<Image> img(new Image());
	img->allocate(m_width, m_height);
	
	const uint size = m_width * m_height;
	for(uint i = 0; i < size; i++) {
		
		uint c;
		uint8 rgba[4];

		for(c = 0; c < num; c++) {
			float f = m_mem[size * (base_component + c) + i];
			rgba[c] = nv::clamp(int(255.0f * f), 0, 255);
		}

		// Fill the rest with 0xff000000;
		for(; c < 4; c++) {
			rgba[c] = c != 3 ? 0 : 0xff;
		}
		
		img->pixel(i) = Color32(rgba[0], rgba[1], rgba[2], rgba[3]);
	}
	
	return img.release();
}


/// Convert the floating point image to a regular image. Correct gamma of rgb, but not alpha.
Image * FloatImage::createImageGammaCorrect(float gamma/*= 2.2f*/) const
{
	nvCheck(m_componentNum == 4);
	
	AutoPtr<Image> img(new Image());
	img->allocate(m_width, m_height);
	
	const float * rChannel = this->channel(0);
	const float * gChannel = this->channel(1);
	const float * bChannel = this->channel(2);
	const float * aChannel = this->channel(3);

	const uint size = m_width * m_height;
	for(uint i = 0; i < size; i++)
	{
		const uint8 r = nv::clamp(int(255.0f * pow(rChannel[i], 1.0f/gamma)), 0, 255);
		const uint8 g = nv::clamp(int(255.0f * pow(gChannel[i], 1.0f/gamma)), 0, 255);
		const uint8 b = nv::clamp(int(255.0f * pow(bChannel[i], 1.0f/gamma)), 0, 255);
		const uint8 a = nv::clamp(int(255.0f * aChannel[i]), 0, 255);

		img->pixel(i) = Color32(r, g, b, a);
	}
	
	return img.release();
}

/// Allocate a 2d float image of the given format and the given extents.
void FloatImage::allocate(uint c, uint w, uint h)
{
	nvCheck(m_mem == NULL);
	m_width = w;
	m_height = h;
	m_componentNum = c;
	m_count = w * h * c;
	m_mem = reinterpret_cast<float *>(nv::mem::malloc(m_count * sizeof(float)));
}

/// Free the image, but don't clear the members.
void FloatImage::free()
{
	nvCheck(m_mem != NULL);
	nv::mem::free( reinterpret_cast<void *>(m_mem) );
	m_mem = NULL;
}

void FloatImage::clear(float f/*=0.0f*/)
{
	for(uint i = 0; i < m_count; i++) {
		m_mem[i] = f;
	}
}

void FloatImage::normalize(uint base_component)
{
	nvCheck(base_component + 3 <= m_componentNum);
	
	float * xChannel = this->channel(base_component + 0);
	float * yChannel = this->channel(base_component + 1);
	float * zChannel = this->channel(base_component + 2);

	const uint size = m_width * m_height;
	for(uint i = 0; i < size; i++) {
		
		Vector3 normal(xChannel[i], yChannel[i], zChannel[i]);
		normal = normalizeSafe(normal, Vector3(zero));
		
		xChannel[i] = normal.x();
		yChannel[i] = normal.y();
		zChannel[i] = normal.z();
	}
}

void FloatImage::packNormals(uint base_component)
{
	scaleBias(base_component, 3, 0.5f, 1.0f);
}

void FloatImage::expandNormals(uint base_component)
{
	scaleBias(base_component, 3, 2, 0.5);
}

void FloatImage::scaleBias(uint base_component, uint num, float scale, float bias)
{
	const uint size = m_width * m_height;
	
	for(uint c = 0; c < num; c++) {
		float * ptr = this->channel(base_component + c);
		
		for(uint i = 0; i < size; i++) {
			ptr[i] = scale * (ptr[i] + bias);
		}
	}
}

/// Clamp the elements of the image.
void FloatImage::clamp(float low, float high)
{
	for(uint i = 0; i < m_count; i++) {
		m_mem[i] = nv::clamp(m_mem[i], low, high);
	}
}

/// From gamma to linear space.
void FloatImage::toLinear(uint base_component, uint num, float gamma /*= 2.2f*/)
{
	exponentiate(base_component, num, gamma);
}

/// From linear to gamma space.
void FloatImage::toGamma(uint base_component, uint num, float gamma /*= 2.2f*/)
{
	exponentiate(base_component, num, 1.0f/gamma);
}

/// Exponentiate the elements of the image.
void FloatImage::exponentiate(uint base_component, uint num, float power)
{
	const uint size = m_width * m_height;

	for(uint c = 0; c < num; c++) {
		float * ptr = this->channel(base_component + c);
		
		for(uint i = 0; i < size; i++) {
			ptr[i] = pow(ptr[i], power);
		}
	}
}

#if 0
float FloatImage::nearest(float x, float y, int c, WrapMode wm) const
{
	if( wm == WrapMode_Clamp ) return nearest_clamp(x, y, c);
	/*if( wm == WrapMode_Repeat )*/ return nearest_repeat(x, y, c);
	//if( wm == WrapMode_Mirror ) return nearest_mirror(x, y, c);
}

float FloatImage::nearest_clamp(int x, int y, const int c) const
{
	const int w = m_width;
	const int h = m_height;
	int ix = ::clamp(x, 0, w-1);
	int iy = ::clamp(y, 0, h-1);
	return pixel(ix, iy, c);
}

float FloatImage::nearest_repeat(int x, int y, const int c) const
{
	const int w = m_width;
	const int h = m_height;
	int ix = x % w;
	int iy = y % h;
	return pixel(ix, iy, c);
}
#endif

float FloatImage::nearest(float x, float y, int c, WrapMode wm) const
{
	if( wm == WrapMode_Clamp ) return nearest_clamp(x, y, c);
	/*if( wm == WrapMode_Repeat )*/ return nearest_repeat(x, y, c);
	//if( wm == WrapMode_Mirror ) return nearest_mirror(x, y, c);
}

float FloatImage::linear(float x, float y, int c, WrapMode wm) const
{
	if( wm == WrapMode_Clamp ) return linear_clamp(x, y, c);
	/*if( wm == WrapMode_Repeat )*/ return linear_repeat(x, y, c);
	//if( wm == WrapMode_Mirror ) return linear_mirror(x, y, c);
}

float FloatImage::nearest_clamp(float x, float y, const int c) const
{
	const int w = m_width;
	const int h = m_height;
	int ix = ::clamp(round(x * w), 0, w-1);
	int iy = ::clamp(round(y * h), 0, h-1);
	return pixel(ix, iy, c);
}

float FloatImage::nearest_repeat(float x, float y, const int c) const
{
	const int w = m_width;
	const int h = m_height;
	int ix = round(frac(x) * w);
	int iy = round(frac(y) * h);
	return pixel(ix, iy, c);
}

float FloatImage::nearest_mirror(float x, float y, const int c) const
{
	// @@ TBD
	return 0.0f;
}

float FloatImage::linear_clamp(float x, float y, const int c) const
{
	const int w = m_width;
	const int h = m_height;
	
	x *= w;
	y *= h;
	
	const float fracX = frac(x);
	const float fracY = frac(y);
	
	const int ix0 = ::clamp(round(x), 0, w-1);
	const int iy0 = ::clamp(round(y), 0, h-1);
	const int ix1 = ::clamp(round(x)+1, 0, w-1);
	const int iy1 = ::clamp(round(y)+1, 0, h-1);

	float f1 = pixel(ix0, iy0, c);
	float f2 = pixel(ix1, iy0, c);
	float f3 = pixel(ix0, iy1, c);
	float f4 = pixel(ix1, iy1, c);
	
	float i1 = lerp(f1, f2, fracX);
	float i2 = lerp(f3, f4, fracX);

	return lerp(i1, i2, fracY);
}

float FloatImage::linear_repeat(float x, float y, int c) const
{
	const int w = m_width;
	const int h = m_height;
	
	const float fracX = frac(x * w);
	const float fracY = frac(y * h);
	
	int ix0 = round(frac(x) * w);
	int iy0 = round(frac(y) * h);
	int ix1 = round(frac(x + 1.0f/w) * w);
	int iy1 = round(frac(y + 1.0f/h) * h);
	
	float f1 = pixel(ix0, iy0, c);
	float f2 = pixel(ix1, iy0, c);
	float f3 = pixel(ix0, iy1, c);
	float f4 = pixel(ix1, iy1, c);
	
	float i1 = lerp(f1, f2, fracX);
	float i2 = lerp(f3, f4, fracX);

	return lerp(i1, i2, fracY);
}

float FloatImage::linear_mirror(float x, float y, int c) const
{
	// @@ TBD
	return 0.0f;
}


/// Fast downsampling using box filter. 
///
/// The extents of the image are divided by two and rounded down.
///
/// When the size of the image is odd, this uses a polyphase box filter as explained in:
/// http://developer.nvidia.com/object/np2_mipmapping.html
///
FloatImage * FloatImage::fastDownSample() const
{
	nvDebugCheck(m_width != 1 || m_height != 1);
	
	AutoPtr<FloatImage> dst_image( new FloatImage() );

	const uint w = max(1, m_width / 2);
	const uint h = max(1, m_height / 2);
	dst_image->allocate(m_componentNum, w, h);

	// 1D box filter.
	if (m_width == 1 || m_height == 1)
	{
		const uint w = m_width * m_height;
		
		if (w & 1)
		{
			const float scale = 1.0f / (2 * w + 1);
			
			for(uint c = 0; c < m_componentNum; c++)
			{
				const float * src = this->channel(c);
				float * dst = dst_image->channel(c);
				
				for(uint x = 0; x < w; x++)
				{
					const float w0 = (w - x);
					const float w1 = (w - 0);
					const float w2 = (1 + x);
					
					*dst++ = scale * (w0 * src[0] + w1 * src[1] + w2 * src[2]);
					src += 2;
				}
			}
		}
		else
		{
			for(uint c = 0; c < m_componentNum; c++)
			{
				const float * src = this->channel(c);
				float * dst = dst_image->channel(c);
				
				for(uint x = 0; x < w; x++)
				{
					*dst = 0.5f * (src[0] + src[1]);
					dst++;
					src += 2;
				}
			}
		}
	}
	
	// Regular box filter.
	else if ((m_width & 1) == 0 && (m_height & 1) == 0)
	{
		for(uint c = 0; c < m_componentNum; c++)
		{
			const float * src = this->channel(c);
			float * dst = dst_image->channel(c);
			
			for(uint y = 0; y < h; y++)
			{
				for(uint x = 0; x < w; x++)
				{
					*dst = 0.25f * (src[0] + src[1] + src[m_width] + src[m_width + 1]);
					dst++;
					src += 2;
				}
				
				src += m_width;
			}
		}
	}
	
	// Polyphase filters.
	else if (m_width & 1 && m_height & 1)
	{
		nvDebugCheck(m_width == 2 * w + 1);
		nvDebugCheck(m_height == 2 * h + 1);
		
		const float scale = 1.0f / (m_width * m_height);
		
		for(uint c = 0; c < m_componentNum; c++)
		{
			const float * src = this->channel(c);
			float * dst = dst_image->channel(c);
			
			for(uint y = 0; y < h; y++)
			{
				const float v0 = (h - y);
				const float v1 = (h - 0);
				const float v2 = (1 + y);
				
				for (uint x = 0; x < w; x++)
				{
					const float w0 = (w - x);
					const float w1 = (w - 0);
					const float w2 = (1 + x);
					
					float f = 0.0f;
					f += v0 * (w0 * src[0 * m_width + 2 * x] + w1 * src[0 * m_width + 2 * x + 1] + w2 * src[0 * m_width + 2 * x + 2]);
					f += v1 * (w0 * src[1 * m_width + 2 * x] + w1 * src[1 * m_width + 2 * x + 1] + w2 * src[0 * m_width + 2 * x + 2]);
					f += v2 * (w0 * src[2 * m_width + 2 * x] + w1 * src[2 * m_width + 2 * x + 1] + w2 * src[0 * m_width + 2 * x + 2]);
					
					*dst = f * scale;
					dst++;
				}
				
				src += 2 * m_width;
			}
		}
	}
	else if (m_width & 1)
	{
		nvDebugCheck(m_width == 2 * w + 1);
		const float scale = 1.0f / (2 * m_width);
		
		for(uint c = 0; c < m_componentNum; c++)
		{
			const float * src = this->channel(c);
			float * dst = dst_image->channel(c);
			
			for(uint y = 0; y < h; y++)
			{
				for (uint x = 0; x < w; x++)
				{
					const float w0 = (w - x);
					const float w1 = (w - 0);
					const float w2 = (1 + x);
					
					float f = 0.0f;
					f += w0 * (src[2 * x + 0] + src[m_width + 2 * x + 0]);
					f += w1 * (src[2 * x + 1] + src[m_width + 2 * x + 1]);
					f += w2 * (src[2 * x + 2] + src[m_width + 2 * x + 2]);
					
					*dst = f * scale;
					dst++;
				}
				
				src += 2 * m_width;
			}
		}
	}
	else if (m_height & 1)
	{
		nvDebugCheck(m_height == 2 * h + 1);
		
		const float scale = 1.0f / (2 * m_height);
		
		for(uint c = 0; c < m_componentNum; c++)
		{
			const float * src = this->channel(c);
			float * dst = dst_image->channel(c);
			
			for(uint y = 0; y < h; y++)
			{
				const float v0 = (h - y);
				const float v1 = (h - 0);
				const float v2 = (1 + y);
				
				for (uint x = 0; x < w; x++)
				{
					float f = 0.0f;
					f += v0 * (src[0 * m_width + 2 * x] + src[0 * m_width + 2 * x + 1]);
					f += v1 * (src[1 * m_width + 2 * x] + src[1 * m_width + 2 * x + 1]);
					f += v2 * (src[2 * m_width + 2 * x] + src[2 * m_width + 2 * x + 1]);
					
					*dst = f * scale;
					dst++;
				}
				
				src += 2 * m_width;
			}
		}
	}
	
	return dst_image.release();
}


/// Downsample applying a 1D kernel separately in each dimension.
FloatImage * FloatImage::downSample(const Kernel1 & kernel, WrapMode wm) const
{
	const uint w = max(1, m_width / 2);
	const uint h = max(1, m_height / 2);
	
	return downSample(kernel, w, h, wm);
}


/// Downsample applying a 1D kernel separately in each dimension.
FloatImage * FloatImage::downSample(const Kernel1 & kernel, uint w, uint h, WrapMode wm) const
{
	nvCheck(!(kernel.width() & 1));	// Make sure that kernel m_width is even.

	AutoPtr<FloatImage> tmp_image( new FloatImage() );
	tmp_image->allocate(m_componentNum, w, m_height);
	
	AutoPtr<FloatImage> dst_image( new FloatImage() );	
	dst_image->allocate(m_componentNum, w, h);
	
	const float xscale = float(m_width) / float(w);
	const float yscale = float(m_height) / float(h);
	
	for(uint c = 0; c < m_componentNum; c++) {
		float * tmp_channel = tmp_image->channel(c);
		
		for(uint y = 0; y < m_height; y++) {
			for(uint x = 0; x < w; x++) {
				
				float sum = this->applyKernelHorizontal(&kernel, uint(x*xscale), y, c, wm);
				
				const uint tmp_index = tmp_image->index(x, y);
				tmp_channel[tmp_index] = sum;
			}
		}
		
		float * dst_channel = dst_image->channel(c);
		
		for(uint y = 0; y < h; y++) {
			for(uint x = 0; x < w; x++) {
				
				float sum = this->applyKernelVertical(&kernel, uint(x*xscale), uint(y*yscale), c, wm);
				
				const uint dst_index = dst_image->index(x, y);
				dst_channel[dst_index] = sum;
			}
		}
	}
	
	return dst_image.release();
}


/// Apply 2D kernel at the given coordinates and return result.
float FloatImage::applyKernel(const Kernel2 * k, int x, int y, int c, WrapMode wm) const
{
	nvDebugCheck(k != NULL);
	
	const uint kernelWidth = k->width();
	const int kernelOffset = int(kernelWidth / 2) - 1;
	
	const float * channel = this->channel(c);

	float sum = 0.0f;
	for(uint i = 0; i < kernelWidth; i++)
	{
		const int src_y = int(y + i) - kernelOffset;
		
		for(uint e = 0; e < kernelWidth; e++)
		{
			const int src_x = int(x + e) - kernelOffset;
			
			int idx = this->index(src_x, src_y, wm);
			
			sum += k->valueAt(e, i) * channel[idx];
		}
	}
	
	return sum;
}


/// Apply 1D vertical kernel at the given coordinates and return result.
float FloatImage::applyKernelVertical(const Kernel1 * k, int x, int y, int c, WrapMode wm) const
{
	nvDebugCheck(k != NULL);
	
	const uint kernelWidth = k->width();
	const int kernelOffset = int(kernelWidth / 2) - 1;
	
	const float * channel = this->channel(c);

	float sum = 0.0f;
	for(uint i = 0; i < kernelWidth; i++)
	{
		const int src_y = int(y + i) - kernelOffset;
		const int idx = this->index(x, src_y, wm);
		
		sum += k->valueAt(i) * channel[idx];
	}
	
	return sum;
}

/// Apply 1D horizontal kernel at the given coordinates and return result.
float FloatImage::applyKernelHorizontal(const Kernel1 * k, int x, int y, int c, WrapMode wm) const
{
	nvDebugCheck(k != NULL);
	
	const uint kernelWidth = k->width();
	const int kernelOffset = int(kernelWidth / 2) - 1;
	
	const float * channel = this->channel(c);

	float sum = 0.0f;
	for(uint e = 0; e < kernelWidth; e++)
	{
		const int src_x = int(x + e) - kernelOffset;
		const int idx = this->index(src_x, y, wm);
		
		sum += k->valueAt(e) * channel[idx];
	}
	
	return sum;
}



#if 0

Vec3d bilinear(double u, double v) const
{
	u = mod(u*(W-1),W);
	v = mod(v*(H-1),H);

	Vec3d v1,v2,v3,v4;

	int x_small	= (int)floor(u);
	int x_big	  = x_small + 1;
	int y_small = (int)floor(v);
	int y_big   = y_small + 1;

	if (x_small < 0)
		x_small = W-1;
	else if (x_big >= W)
		x_big = 0;
	if (y_small < 0)
		y_small = H-1;
	else if (y_big >= H)
		y_big = 0;
	
	double fractional_X = u - x_small;
	double fractional_Y = v - y_small;

	if (nchan == 3)
	{
		v1 = Vec3d(pixel(x_small, y_small)[0], pixel(x_small, y_small)[1], pixel(x_small, y_small)[2]);
		v2 = Vec3d(pixel(x_big, y_small)[0], pixel(x_big, y_small)[1], pixel(x_big, y_small)[2]);
		v3 = Vec3d(pixel(x_small, y_big)[0], pixel(x_small, y_big)[1], pixel(x_small, y_big)[2]);
		v4 = Vec3d(pixel(x_big, y_big)[0], pixel(x_big, y_big)[1], pixel(x_big, y_big)[2]);
	}
			
	Vec3d i1 = lerp(v1, v2, fractional_X);
	Vec3d i2 = lerp(v3, v4, fractional_X);

	return lerp(i1, i2, fractional_Y);
}

Vec3d bicubic(double u, double v) const
{
	u = mod(u*(W-1),W);
	v = mod(v*(H-1),H);

	int x_small1	= (int)floor(u),
		x_small2	= x_small1 - 1,
		x_big1		= x_small1 + 1,				
		x_big2		= x_small1 + 2;

	int y_small1	= (int)floor(v),
		y_small2	= y_small1 - 1,
		y_big1		= y_small1 + 1,
		y_big2		= y_small1 + 2;

	x_small1	= (int)mod(x_small1,W);
	x_small2	= (int)mod(x_small2,W);
	x_big1		= (int)mod(x_big1,W);
	x_big2		= (int)mod(x_big2,W);
	
	y_small1	= (int)mod(y_small1,H);
	y_small2	= (int)mod(y_small2,H);
	y_big1		= (int)mod(y_big1,H);
	y_big2		= (int)mod(y_big2,H);
	
	double fractional_X = u - x_small1;
	double fractional_Y = v - y_small1;

	if (nchan == 3)
	{
		// the interpolations across the rows
		Vec3d row1 = cubic(Vec3d(pixel(x_small2, y_small2)[0], pixel(x_small2, y_small2)[1], pixel(x_small2, y_small2)[2]),
							Vec3d(pixel(x_small1, y_small2)[0], pixel(x_small1, y_small2)[1], pixel(x_small1, y_small2)[2]),
							Vec3d(pixel(x_big1, y_small2)[0], pixel(x_big1, y_small2)[1], pixel(x_big1, y_small2)[2]),
							Vec3d(pixel(x_big2, y_small2)[0], pixel(x_big2, y_small2)[1], pixel(x_big2, y_small2)[2]),
							fractional_X);

		Vec3d row2 = cubic(Vec3d(pixel(x_small2, y_small1)[0], pixel(x_small2, y_small1)[1], pixel(x_small2, y_small1)[2]),
							Vec3d(pixel(x_small1, y_small1)[0], pixel(x_small1, y_small1)[1], pixel(x_small1, y_small1)[2]),
							Vec3d(pixel(x_big1, y_small1)[0], pixel(x_big1, y_small1)[1], pixel(x_big1, y_small1)[2]),
							Vec3d(pixel(x_big2, y_small1)[0], pixel(x_big2, y_small1)[1], pixel(x_big2, y_small1)[2]),
							fractional_X);

		Vec3d row3 = cubic(Vec3d(pixel(x_small2, y_big1)[0], pixel(x_small2, y_big1)[1], pixel(x_small2, y_big1)[2]),
							Vec3d(pixel(x_small1, y_big1)[0], pixel(x_small1, y_big1)[1], pixel(x_small1, y_big1)[2]),
							Vec3d(pixel(x_big1, y_big1)[0], pixel(x_big1, y_big1)[1], pixel(x_big1, y_big1)[2]),
							Vec3d(pixel(x_big2, y_big1)[0], pixel(x_big2, y_big1)[1], pixel(x_big2, y_big1)[2]),
							fractional_X);

		Vec3d row4 = cubic(Vec3d(pixel(x_small2, y_big2)[0], pixel(x_small2, y_big2)[1], pixel(x_small2, y_big2)[2]),
							Vec3d(pixel(x_small1, y_big2)[0], pixel(x_small1, y_big2)[1], pixel(x_small1, y_big2)[2]),
							Vec3d(pixel(x_big1, y_big2)[0], pixel(x_big1, y_big2)[1], pixel(x_big1, y_big2)[2]),
							Vec3d(pixel(x_big2, y_big2)[0], pixel(x_big2, y_big2)[1], pixel(x_big2, y_big2)[2]),
							fractional_X);

		// now interpolate across the interpolated rows (the columns)

		return cubic(row1,row2,row3,row4,fractional_Y);
	}
	else
		return Vec3d(0.0);
}

Vec3d bicubic2(double u, double v) const
{
	u = mod(u*(W-1),W);
	v = mod(v*(H-1),H);

	int x_small1	= floorf(u),
		x_small2	= x_small1 - 1,
		x_big1		= int(x_small1 + 1),
		x_big2		= int(x_small1 + 2);

	int y_small1	= floorf(v),
		y_small2	= y_small1 - 1,
		y_big1		= y_small1 + 1,
		y_big2		= y_small1 + 2;

	x_small1	= (int)mod(x_small1,W);
	x_small2	= (int)mod(x_small2,W);
	x_big1		= (int)mod(x_big1,W);
	x_big2		= (int)mod(x_big2,W);
	
	y_small1	= (int)mod(y_small1,H);
	y_small2	= (int)mod(y_small2,H);
	y_big1		= (int)mod(y_big1,H);
	y_big2		= (int)mod(y_big2,H);
	
	double fractional_X = u - x_small1;
	double fractional_Y = v - y_small1;

	if (nchan == 3)
	{
		// the interpolations across the rows
		Vec3d row1 = cubic2(Vec3d(pixel(x_small2, y_small2)[0], pixel(x_small2, y_small2)[1], pixel(x_small2, y_small2)[2]),
							Vec3d(pixel(x_small1, y_small2)[0], pixel(x_small1, y_small2)[1], pixel(x_small1, y_small2)[2]),
							Vec3d(pixel(x_big1, y_small2)[0], pixel(x_big1, y_small2)[1], pixel(x_big1, y_small2)[2]),
							Vec3d(pixel(x_big2, y_small2)[0], pixel(x_big2, y_small2)[1], pixel(x_big2, y_small2)[2]),
							fractional_X);

		Vec3d row2 = cubic2(Vec3d(pixel(x_small2, y_small1)[0], pixel(x_small2, y_small1)[1], pixel(x_small2, y_small1)[2]),
							Vec3d(pixel(x_small1, y_small1)[0], pixel(x_small1, y_small1)[1], pixel(x_small1, y_small1)[2]),
							Vec3d(pixel(x_big1, y_small1)[0], pixel(x_big1, y_small1)[1], pixel(x_big1, y_small1)[2]),
							Vec3d(pixel(x_big2, y_small1)[0], pixel(x_big2, y_small1)[1], pixel(x_big2, y_small1)[2]),
							fractional_X);

		Vec3d row3 = cubic2(Vec3d(pixel(x_small2, y_big1)[0], pixel(x_small2, y_big1)[1], pixel(x_small2, y_big1)[2]),
							Vec3d(pixel(x_small1, y_big1)[0], pixel(x_small1, y_big1)[1], pixel(x_small1, y_big1)[2]),
							Vec3d(pixel(x_big1, y_big1)[0], pixel(x_big1, y_big1)[1], pixel(x_big1, y_big1)[2]),
							Vec3d(pixel(x_big2, y_big1)[0], pixel(x_big2, y_big1)[1], pixel(x_big2, y_big1)[2]),
							fractional_X);

		Vec3d row4 = cubic2(Vec3d(pixel(x_small2, y_big2)[0], pixel(x_small2, y_big2)[1], pixel(x_small2, y_big2)[2]),
							Vec3d(pixel(x_small1, y_big2)[0], pixel(x_small1, y_big2)[1], pixel(x_small1, y_big2)[2]),
							Vec3d(pixel(x_big1, y_big2)[0], pixel(x_big1, y_big2)[1], pixel(x_big1, y_big2)[2]),
							Vec3d(pixel(x_big2, y_big2)[0], pixel(x_big2, y_big2)[1], pixel(x_big2, y_big2)[2]),
							fractional_X);

		// now interpolate across the interpolated rows (the columns)

		return cubic2(row1,row2,row3,row4,fractional_Y);
	}
	else
		return Vec3d(0.0);
}

#endif