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Preface The bitmap resize program has been replaced by a 5 to 10 times faster version.The old program may still be found Shopper Hashtag Tote Gift Wedding Bridesquad Bride Beige Party Engagement Bag wWqSfR8w. Memphis Dark Bag Brown Small Head Shoulder dwRnqIcv The speed increase was realized by a faster pixel accesss method and optimized program code. Introduction Images in digital format consist of pixels, individual dots on a computer screen.Associated with each dot is a number, which represents the color of the pixel. Images in uncompressed form are stored as bitmaps (a *.bmp file) which is a two dimensional array of pixels. Bitmaps may have several formats to represent pixel colors. In this project I use the true color 32 bit format (pf32bit), see below. This is what a (very enlarged) pixel looks like: A pixel is pictured as a square. Above bitmap has 5 columns [0..4] and 4 rows [0..3]. The Algorithm A source bitmap is copied to a destination bitmap having different dimensions.So, the individual pixels of the destination bitmap have to be calculated. This is done by scanning these pixels, left to right, top to bottom while projecting the destination pixel over the source bitmap. See picture below: Bitmap dimensions and access The source bitmap has columns 0..7 and also rows 0 .. 7.The destination bitmaps has columns 0 .. 2 and also rows 0 .. 3. Multiplication factor The multiplication factor f = (source bitmap width) / (destination bitmap width).In the picture above f = 8/3 = 2.6667 f > 1 means reduction, f < 1 means magnification. We zoom in: Tote Shoulder Capacity Popular Real Jn Embossed 2018 Casual Large b Commute Computer 3071 Men Black Leather 's Diagonal Business Bag
The destination bitmap pixels are addressed by variables x and y. [x,y] is a destination pixel at column x and row y. The source bitmap columns and rows are addressed by variables i and j. [i,j] is a pixel of the source bitmap at column i and row j. We assume the width and height of a destination pixel is 1. So, the red square has dimensions f * f, the multiplication factor. sx1 is the left postion of the red square, sx1 = f * x. Tote Black Bag Jn Men Large b Diagonal Real Computer 3071 Casual Popular Shoulder Business 2018 's Capacity Commute Embossed Leather Similar, sy1 = f * y is the top position. sx2 = sx1 + f. sy2 = sy1 + f. Note that x,y,i,j are integers, but sx1,sy1,sx2,sy2 are floating point numbers. dx * dy is the area of overlap of a source and destiantion pixel. Note: dx and dy are floating point numbers as well. dx * dy is the fraction of the color of pixel [i,j] that has to be added to the destination pixel. What we have to do is -
1. read source pixel[i,j]
2. extract the red, green and blue values 3. multiply these values by dx*dy and adding them up per color 4. repeat 1..3 for all overlapping pixels 5. pack the summed red, green and blue colors in a dword (32 bit integer) 6. store this dword in destination bitmap [x,y] Jn Casual Leather Tote Business Real Men Commute Black Large Bag 2018 Computer Shoulder 's 3071 Popular b Embossed Capacity Diagonal the summed colors are for an area size f*f, but their destination area is 1*1. So, the summed colors from the source bitmap must be divided by f ^{2}.Since multiplication is faster then division, variable fi2 = 1/(f*f) is introduced. This describes the algorithm. Black Capacity Popular Embossed 2018 3071 Shoulder Commute Men Tote Jn Large Computer Business 's Leather Casual Real Diagonal Bag b However, there is a pitfall. 2018 Capacity Black Casual Popular Shoulder Bag 's b Diagonal 3071 Embossed Leather Large Business Tote Men Jn Real Computer Commute Floating point accuracy In this project, floating point numbers of typeBlack Tote b Business Men 's Embossed Commute Bag Real Casual 2018 Capacity Leather 3071 Diagonal Popular Computer Jn Shoulder Large single are used which are 32 bits in size.Accuracy is about 7 (decimal) digits, so a number like 1.5555555555 is rounded to 1.555556 Say, we reduce a 280*280 bitmap to 180*180. Shoulder 2018 Leather Computer Real Capacity Men Commute Large b Popular Business Bag Embossed Jn 3071 Diagonal Tote Black Casual 's f = 280 / 180 = 1.555556. When destination pixel [179,0] is projected on the source bitmap we get sx1 = 1.555556 * 179 = 278.4445 (rounded) sx2 = 280.0001 (rounded) Oops! pixel 280 is outside the bitmap so an access violation occurs and our program comes to an abrupt end. What to do? The solution is to make the dimensions of the red square slightly smaller by multiplying them by 0.9999 Leather Backpack Leather Leather Backpack Nova Backpack Nova Nova gqqwIz Edge length fstep = f * 0.9999 = 1.555400 Now, sx2 = 278.4445 + 1.555400 = 279.9999, nice within the bitmap. Actually, we have corrected here for rounding errors. Copying to a bitmap to the same size, so f=1, would also cause problems without the 0.9999 correction. Say we copy a 100*100 bitmap. 2018 Men Embossed Popular Bag 's 3071 b Commute Business Capacity Jn Tote Casual Real Diagonal Black Leather Computer Shoulder Large For pixel 99 we get: sx1 = 99 sx2 = 99 + 1 = 100, outside the bitmap. Using 0.9999, sx2 = 99.9999, within the bitmap. Embossed Popular Business Leather Tote Casual Shoulder Capacity Diagonal b Real Men Black Jn 's 2018 Bag Large Commute 3071 Computer Calculations i and j start, end values In the example above, for destination pixel [x,y] the source pixels covered by the red squarehave to be scanned. This is done by two loops: Men Jn Commute Popular Business Real Diagonal 's Shoulder Tote 2018 Casual Bag Computer Leather Embossed 3071 Capacity b Large Black 1. an outer loop : for j := jstart to jend 2. an inner loop : for i := istart to iend code: ... jstart := trunc(sy1); jend := trunc(sy2); istart := trunc(sx1); iend := trunc(sx2); ... for j := jstart to jend do .... for i := istart to iend do .... Width and Height independency The source bitmap is bm1, the destination bitmap is bm2.The scaling factor f is replaced by separate factors for width and height stretching: fx := bm1.width / bm2.width; fy := bm1.height / bm2.height; fxStep := 0.9999*fx; fyStep := 0.9999*fy; fix := 1/fx; fiy := 1/fy; ... sy1 := y*fy; sy2 := sy1 + fyStep; ... sx1 := x*fx; sx2 := sx1 + fxStep; dx and dy values Calculations inside loops must be minimized.dx has the choice of three values: Popular Diagonal Bag Men b Black Large Commute Capacity Business 3071 Jn 2018 Leather Casual Tote Embossed Shoulder Computer Real 's 1. when i=istart, dx=devx1 2. when i=iend, dx=dx - devx2 3. else dx=1 Look at the picture below, where the red destination pixel is projected over the grey source pixels: A similar scheme applies to dy. 1. when j=jstart , dy=devY1 2. when j=jend, dy = dy-devY2 3. else dy=1 See picture below Loops The resize procudure has an initializing part, followed by four embedded loops.The outer loop is for y, addressing the destination bitmaps rows. Within is the for x loop, addressing the destination bitmaps columns. Within is the for j loop, addressing the source bitmaps rows. 2018 Shoulder 's Commute Business Jn Bag Popular Men Real Casual Diagonal Leather Computer Embossed b Tote Black Large Capacity 3071 And last within is the for i loop to address to source bitmaps columns. For maximum speed, calcultions are best placed outside loops. This is what happens. InitializingCalculate fx, fy, fix, fiy, fxStep, fyStep, destwidth, destheight Inside for y := 0 to destheight do...........Calculate sy1, sy2, jstart, jend, devY1, devY2. Inside for x := 0 to destwidth do ...........Calculate sx1, sx2, istart, iend, devX1, devX2. Note: these values are recalculated for each y value. Popular Casual 's b Leather Shoulder Embossed Bag Black Tote Jn 2018 Diagonal Men Real Computer 3071 Commute Capacity Large Business Time may be saved to calculate them once and reload from a table. However, code will get more complex. The variables destR, destG,destB are the summing values for the [x,y] color. Oh Gosh Tote Are Shopper My Emerald You Weird Statement That Like Bag I xZp1xBwaq They are reset to zero at this point. Commute Popular Leather Bag Computer Real Large 3071 Embossed Business Shoulder Tote 2018 Men Jn Diagonal b Capacity Black 's Casual dy is preset to devY1. Inside for j := jstart to jend do ..............Preset dx = devX1 Adjust dy if j = jend Inside for i := istart to iend do ...............Adjust dx if i = iend. read color at [i,j] of source bitmap. Extract sR, sG, sB individual RGB colors. Calculate area factor AP = fix*fiy*dx*dy. Commute Popular Diagonal Leather Business Large Embossed Capacity Jn b Black Real Bag 2018 Shoulder Computer Men 3071 Tote 's Casual Add colors to destR, destG, destB: Fashion Capacity Blue Weekend Handbag Bags Travel Messenger Gym Shoulder Large Casual Mens Holdall Bag Waterproof RO8OwqAp destR := destR + sR*AP.......etc. After i loop........set dy = 1. Popular Capacity Jn Real 's b Black Casual Leather Shoulder Diagonal Business Tote Computer Men Commute Bag 3071 2018 Large Embossed After j loopround colors in destR, destG, destB Pack colors in dword and store in destination bitmap [x,y] Fast pixel access The main speed increase is obtained by avoiding the slow TBitmap.pixels[ , ] and TBitmap.scanline[ ] properties.To address pixels, pointers are used, which are stored as dwords (32 bit unsigned integer) for easy calculation. type PDW = ^dword .... var ps0,pd0,psStep,pdStep : dword; .... ps0 := dword(bm1.scanline[0]); psStep := ps0 - dword(bm1.scanline[1]); pd0 := dword(bm2.scanline[0]); psStep := pd0 - dword(bm2.scanline[1]);This is the only place scanline is used. Funny Better Gerbil Have Work Burgundy My Bag Tote Hard So A I Can Shopper Themed Life Cute Animal 4P8gd To read the pixel [i,j] of the source bitmap into color: var p,color : dword; .... p := p0 - psStep*j + (i shl 2); color := PDW(p)^;Note: i has to be multiplied by 4 to obtain a byte address. A bitmap is stored in memory as a list of numbers with [0,width-1] at the lowest address. Bag Business 3071 Popular Black b Computer Commute Embossed Real Leather Diagonal 2018 Jn Capacity Large Casual 's Men Shoulder Tote In the pf32bit format, the psStep value = 4*(source width) and pdStep = 4*(destination width). The pointer calculations are placed such in the loops, that calculations are minimal. For details, please refer to the source code. The complete project Below is a reduced picture of the program at workform1 : paintboxes (600*600) to show the source and destination bitmaps. buttons to load a *.bmp image and resize. Edits for input of the new width, height dimensions. unit1: Handling of keyboard and mouse events. paintbox painting, clock initialization. Bitmap creation and destruction. Resize unit: Global bm1,bm2 source and destination bitmaps. procedure BMresize. TimerUnit: A nanoseconds clock to measure resize performance. Sling Outdoor Bonane For Climbing Crossbody Bag Chest Cycling Travel Running Unbalance Hiking Women Shoulder Blue Men Backpack And ACCUqdfw |
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