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Top Forums Shell Programming and Scripting Script to solve second order (polynomial) interpolation Post 302759197 by Tzeronone on Monday 21st of January 2013 08:59:06 PM
Old 01-21-2013
Quote:
Originally Posted by Corona688
What do you mean by polynomial interpolation?

Polynomial interpolation is an interpolation that based on three value points (two previous points and next point). So, if we see the data, there are an ID 1, 4, and 8. So, we need to find out the value of 2, 3, 5, 6, and 7 based on value 1, 4, and 8. The formula is that
(((x-x2) * (x-x3)) / ((x1-x2) * (x1-x3))) * y1 + (((x-x1) * (x-x3)) / ((x2-x1) * (x2-x3))) * y2 + (((x-x1) * (x-x2)) / ((x3-x1) * (x3-x1))) * y3
x = current ID;
x1 = the first known ID (second previous known ID); ---> 1
x2 = the second known ID (first previous known ID); ---> 4
x3 = the third known ID (next known ID); ---> 8
y1 = the first known value (the value of ID x1)
y2 = the second known value (the value of ID x2)
y3 = the third known value (the value of ID x3)
 

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mlib_ImageZoomTranslateTableBlend(3MLIB)		    mediaLib Library Functions			  mlib_ImageZoomTranslateTableBlend(3MLIB)

NAME
mlib_ImageZoomTranslateTableBlend - image scaling using interpolation table, combined with alpha blending SYNOPSIS
cc [ flag... ] file... -lmlib [ library... ] #include <mlib.h> mlib_status mlib_ImageZoomTranslateTableBlend(mlib_image *dst, const mlib_image *src, mlib_d64 zoomx, mlib_d64 zoomy, mlib_d64 tx, mlib_d64 ty, const void *table, mlib_edge edge, mlib_blend blend, mlib_s32 cmask); DESCRIPTION
The mlib_ImageZoomTranslateTableBlend() function will enlarge or minify the source image by the X and Y zoom factors, with translation, and blend it with the destination image. It uses the following equation for coordinate mapping: xd = zoomx*xs + tx yd = zoomy*ys + ty where a point with coordinates (xs, ys) in the source image is mapped to a point with coordinates (xd, yd) in the destination image. The center of the upper-left corner pixel of an image is located at (0.5, 0.5). It is assumed that the overall alpha for controlling the blending between the source image and the destination image has been pre-multi- plied to the interpolation table for better performance. The alpha blending is closely combined with the interpolation to achieve better performance. Part of alpha blending has to be performed before or together with the interpolation if the source image has an alpha channel. In that case, the color components of each neighboring source pixel which participates in the interpolation (src_r and etc.) have to be pre-multiplied by the alpha component of the same source pixel (src_a). After the interpolation, the interpolated alpha (interp_a, which has been multiplied by the overall alpha because of the pre-multiplied interpolation table) and the destination pixel's original alpha (dst_a, if any) are used to blend the interpolated source pixel (with components interp_r and etc.) with the destination pixel (with components dst_r and etc.). The MLIB_BLEND_GTK_SRC blending is similar to the SRC rule of the Porter-Duff rules for image compositing. It is defined by Cd = Cs Ad = As in general, and by the following formula for this function: if (interp_a != 0.0) { if (dst_has_alpha) { dst_r = interp_r/interp_a; dst_g = interp_g/interp_a; dst_b = interp_b/interp_a; dst_a = interp_a; } else { dst_r = interp_r; dst_g = interp_g; dst_b = interp_b; dst_a = 1.0; // implied } } else { dst_r = 0; dst_g = 0; dst_b = 0; dst_a = 0; } The MLIB_BLEND_GTK_SRC_OVER or MLIB_BLEND_GTK_SRC_OVER2 blending is similar to the SRC_OVER rule of the Porter-Duff rules for image com- positing. It is defined by Cd = Cs + Cd*(1 - As) Ad = As + Ad*(1 - As) in general, and by the following formula for this function: w = interp_a + (1 - interp_a)*dst_a; if (w != 0.0) { dst_r = (interp_r + (1 - interp_a)*dst_a*dst_r)/w; dst_g = (interp_g + (1 - interp_a)*dst_a*dst_g)/w; dst_b = (interp_b + (1 - interp_a)*dst_a*dst_b)/w; dst_a = w; } else if (MLIB_BLEND_GTK_SRC_OVER) { dst_r = 0; dst_g = 0; dst_b = 0; dst_a = 0; } where src_a, interp_a and dst_a are assumed to be in the range of [0.0, 1.0]. For an image with 4 channels, the first or the fourth channel is considered the alpha channel if cmask equals 8 or 1, respectively. An image with 3 channels is considered to have no alpha channel, which is equivalent to having an alpha channel filled with all 1.0, or 0xff in case of MLIB_BYTE, if the general formulas for blending shown above are used. Both src and dst must be of type MLIB_BYTE. They can have either 3 or 4 channels. The src image cannot have width or height larger than 32767. PARAMETERS
The function takes the following arguments: dst Pointer to destination image. src Pointer to first source image. zoomx X zoom factor. zoomx > 0.0. zoomy Y zoom factor. zoomy > 0.0. tx X translation. ty Y translation. table Pointer to interpolation table structure. edge Type of edge condition. It can be one of the following: MLIB_EDGE_DST_NO_WRITE MLIB_EDGE_DST_FILL_ZERO MLIB_EDGE_OP_NEAREST MLIB_EDGE_SRC_EXTEND MLIB_EDGE_SRC_EXTEND_INDEF MLIB_EDGE_SRC_PADDED blend Type of alpha blending. It can be one of the following: MLIB_BLEND_GTK_SRC MLIB_BLEND_GTK_SRC_OVER MLIB_BLEND_GTK_SRC_OVER2 cmask Channel mask to indicate the alpha channel. RETURN VALUES
The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE. ATTRIBUTES
See attributes(5) for descriptions of the following attributes: +-----------------------------+-----------------------------+ | ATTRIBUTE TYPE | ATTRIBUTE VALUE | +-----------------------------+-----------------------------+ |Interface Stability |Evolving | +-----------------------------+-----------------------------+ |MT-Level |MT-Safe | +-----------------------------+-----------------------------+ SEE ALSO
mlib_ImageZoomBlend(3MLIB), mlib_ImageZoomTranslateBlend(3MLIB), mlib_ImageInterpTableCreate(3MLIB), attributes(5) SunOS 5.10 10 Nov 2004 mlib_ImageZoomTranslateTableBlend(3MLIB)
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