英文:
Midpoint ellipse algorithm in 8086 Assembly
问题
我正在尝试使用8086汇编在VGA（320x200）模式下实现椭圆绘制算法，但对于较大的半径，形状绘制不正确。
如图所示，形状是凹陷的，而不是椭圆形状。当轴的长度较小时，例如（10，15），我得到了可接受的结果，但超过这个范围后，它停止呈现椭圆形状。我使用FPU计算所有值。
SCREEN_WIDTH = 320SCREEN_HEIGHT = 200HALF_SCREEN_WIDTH = SCREEN_WIDTH / 2HALF_SCREEN_HEIGHT = SCREEN_HEIGHT / 2x_radius dw 40 ;椭圆宽度y_radius dw 50 ;椭圆高度x_derivative dw ? ;由椭圆方程计算的导数y_derivative dw ?x_squared dw ? ;为方便起见的平方值y_squared dw ?decision_param dw ?four dw 4 ;一些表达式中使用的整数值two dw 2 ;存储它们以便将它们加载到FPUcalc_x_derivative:;x_derivative = 2 * y_squared * x;RPN: 2 y_squared x * *calc_y_derivative:;y_derivative = 2 * x_squared * y;RPN: 2 x_squared y * *ellipse:;初始化x为0，y为y_radius;...calc_decision_param_1:;d1 = y_squared - (x_squared * ry) + (1/4 * x_squared);RPN: y_squared x_squared ry * - x_squared 4 / +;...region_1_loop:;...calc_decision_param_2:;decision_param = (y_squared * (x + 1/2) * (x + 1/2)) + (x_squared * (y - 1) * (y - 1)) - (x_squared * y_squared);RPN: y_squared x 1 2 / + * x 1 2 / + * x_squared y 1 - * y 1 - * + x_squared y_squared * -;...region_2_loop:;...end_program:;...clear_screen:;...
我尝试了许多不同版本的相同算法，但都没有成功。我认为问题可能出在我的变量上（特别是导数和决策参数），可能是溢出的问题。我尝试通过使用double words而不是words声明变量来修复它，但后来在算法中比较它们时遇到了问题，即使成功编译程序，它仍然不能按预期工作。
英文:
I'm trying to implement an ellipse drawing algorithm with 8086 Assembly in VGA (320x200) mode, but the shape is not drawing properly for bigger radii.
As you can see the shape is concave or straight not elliptical. I get acceptable result when the axis have small lengths i.e (10, 15) but any more then that and it stops resembling an ellipse. I used an FPU to calculate all values.
.387SCREEN_WIDTH = 320SCREEN_HEIGHT = 200HALF_SCREEN_WIDTH = SCREEN_WIDTH / 2HALF_SCREEN_HEIGHT = SCREEN_HEIGHT / 2stack1 segment stackdw 300 dup(?)stack_top dw ? ;stack_top pointerstack1 endscode1 segmentstart1:mov ax,seg stack1mov ss,ax ; initialize stackmov sp, offset stack_topmov al, 13hmov ah, 0 ; change modeint 10h ; enter graphics modemov byte ptr cs:[color], 10start_draw:call clear_screencall ellipsewait_key:in al, 60h ;take keyboard inputcmp al, 1 ;if ESC endje end_programjmp wait_key;-------------------------------------------------------------;-------------------------------------------------------------x_radius dw 40 ;width of the ellipsey_radius dw 50 ;height of the ellipsex_derivative dw ? ;derivates calculated from ellipse equationy_derivative dw ?x_squared dw ? ;squared values for conveniencey_squared dw ?decision_param dw ?four dw 4 ;int values used in some of the expressionstwo dw 2 ;storing them so I can load them to the FPU;----------------------calc_x_derivative:;x_derivative = 2 * y_squared * x;RPN: 2 y_squared x * *finitfild word ptr cs:[y_squared]fimul word ptr cs:[two] ;instead of multiplying by 2fimul word ptr cs:[x]fistp word ptr cs:[x_derivative]retcalc_y_derivative:;y_derivative = 2 * x_squared * y;RPN: 2 x_squared y * *finitfild word ptr cs:[x_squared]fimul word ptr cs:[two]fimul word ptr cs:[y]fistp word ptr cs:[y_derivative]retellipse:;initialize x as 0 and y as y_radiusmov word ptr cs:[x], 0mov ax, word ptr cs:[y_radius]mov word ptr cs:[y], axx_radius_squared:finitfild word ptr cs:[y_radius]fimul word ptr cs:[y_radius]fistp word ptr cs:[y_squared]y_radius_squared:finitfild word ptr cs:[x_radius]fimul word ptr cs:[x_radius]fistp word ptr cs:[x_squared]derivatives:call calc_x_derivativecall calc_y_derivativecalc_decision_param_1:;d1 = y_squared - (x_squared * ry) + (1/4 * x_squared);RPN: y_squared x_squared ry * - x_squared 4 / +finitfild word ptr cs:[y_squared]fild word ptr cs:[x_squared]fild word ptr cs:[y_radius]fmulfsubfild word ptr cs:[x_squared]fidiv word ptr cs:[four]faddfistp word ptr cs:[decision_param]region_1_loop:call color_all_symmetriesinc word ptr cs:[x]call calc_x_derivativecmp word ptr cs:[decision_param], 0 ;compare decision_param to 0jge region_1_alternative_next ;if its lower decrement y and calculate alternative decision_paramregion_1_next:;decision_param = decision_param + x_derivative + (y_squared);RPN: decision_param x_derivative + y_squared +finitfild word ptr cs:[decision_param]fild word ptr cs:[x_derivative]faddfild word ptr cs:[y_squared]faddfistp word ptr cs:[decision_param]jmp region_1_loop_endregion_1_alternative_next:;decision_param = decision_param + x_derivative - y_derivative + (y_squared);RPN: decision_param x_derivative + y_derivative - y_squared +dec word ptr cs:[y]call calc_y_derivativefinitfild word ptr cs:[decision_param]fild word ptr cs:[x_derivative]faddfild word ptr cs:[y_derivative]fsubfild word ptr cs:[y_squared]faddfistp word ptr cs:[decision_param]region_1_loop_end:mov ax, word ptr cs:[x_derivative]cmp ax, word ptr cs:[y_derivative] ;check if x_derivative < y_derivativejge calc_decision_param_2 ;if it is we are done with region 1jmp region_1_loopcalc_decision_param_2:;decision_param = (y_squared * (x + 1/2) * (x + 1/2)) + (x_squared * (y - 1) * (y - 1)) - (x_squared * y_squared);RPN: y_squared x 1 2 / + * x 1 2 / + * x_squared y 1 - * y 1 - * + x_squared y_squared * -fild word ptr cs:[y_squared]fild word ptr cs:[x]fld1fidiv word ptr cs:[two]faddfmulfild word ptr cs:[x]fld1fidiv word ptr cs:[two]faddfmulfild word ptr cs:[x_squared]fild word ptr cs:[y]fld1fsubfmulfild word ptr cs:[y]fld1fsubfmulfaddfild word ptr cs:[x_squared]fimul word ptr cs:[y_squared]fsubfistp word ptr cs:[decision_param]region_2_loop:call color_all_symmetriesdec word ptr cs:[y]call calc_y_derivativecmp word ptr cs:[decision_param], 0 ;check if decision_param < 0jge alternative_region_2_nextregion_2_next:;decision_param = decision_param + x_squared - y_derivative;RPN: decision_param x_squared + y_derivative -finitfild word ptr cs:[decision_param]fild word ptr cs:[x_squared]faddfild word ptr cs:[y_derivative]fsubfistp word ptr cs:[decision_param]jmp region_2_loop_endalternative_region_2_next:inc word ptr cs:[x]call calc_x_derivativeregion_2_alternative_decision_param:;decision_param = decision_param + x_derivative - y_derivative + (x_squared);RPN: decision_param x_derivative + y_derivative - x_squared +finitfild word ptr cs:[decision_param]fild word ptr cs:[x_derivative]faddfild word ptr cs:[y_derivative]fsubfild word ptr cs:[x_squared]faddfistp word ptr cs:[decision_param]region_2_loop_end:;y_derivative = y_derivative - (2 * x_squared);RPN: y_derivative 2 x_squared * -finitfild word ptr cs:[y_derivative]fild word ptr cs:[two]fild word ptr cs:[x_squared]fmulfsubfistp word ptr cs:[y_derivative]cmp word ptr cs:[y], 0 ; check if y <= 0jg region_2_loopend_ellipse:ret;-------------------------------------------------------------;--------------------- color_pixel -------------------------x dw ?y dw ?temp_y dw ?temp_x dw ?color db ?;---------------------color_all_symmetries:; Coloring points (xc + x, yc + y), (xc - x, yc + y), (xc + x, yc - y), (xc - x, yc - y)push ax;Point (xc + x, yc - y)mov ax, HALF_SCREEN_HEIGHTsub ax, word ptr cs:[y]mov word ptr cs:[temp_y], axmov ax, word ptr cs:[x]add ax, HALF_SCREEN_WIDTHmov word ptr cs:[temp_x], axcall color_pixel;Point (xc - x, yc - y)mov ax, HALF_SCREEN_HEIGHTsub ax, word ptr cs:[y]mov word ptr cs:[temp_y], axmov ax, HALF_SCREEN_WIDTHsub ax, word ptr cs:[x]mov word ptr cs:[temp_x], axcall color_pixel;Point (xc + x, yc + y)mov ax, HALF_SCREEN_HEIGHTadd ax, word ptr cs:[y]mov word ptr cs:[temp_y], axmov ax, word ptr cs:[x]add ax, HALF_SCREEN_WIDTHmov word ptr cs:[temp_x], axcall color_pixel;Point (xc - x, yc - y)mov ax, HALF_SCREEN_HEIGHTadd ax, word ptr cs:[y]mov word ptr cs:[temp_y], axmov ax, HALF_SCREEN_WIDTHsub ax, word ptr cs:[x]mov word ptr cs:[temp_x], axcall color_pixelpop axretcolor_pixel:push axpush es;position needs to be in a format y*320 + xmov ax, 0a000hmov es, axmov ax, word ptr cs:[temp_y] ;selecting a rowmov bx, SCREEN_WIDTHmul bx ;ax multiplying y by 320 to get proper positionmov bx, word ptr cs:[temp_x] ;selecting a columnadd bx, ax ;adding to the pixel positionmov al, byte ptr cs:[color] ;adding a colormov byte ptr es:[bx], alpop espop axret;-------------------------------------------------------------end_program:mov al, 3hmov ah, 0int 10hmov ax, 4c00hint 21hclear_screen:mov ax, 0a000hmov es, axxor ax, axmov di, axmov cx, SCREEN_WIDTH * SCREEN_HEIGHTmov al, 0cldrep stosb ;while cx != 0, mov byte ptr es:[di], al; di++; cx--retcode1 endsend start1
I tried many different version of the same algorithm all to no success. I think it might be an issue with my variables(especially the derivatives and decision parameter) overflowing I tried fixing it by using double words instead of words to declare variables but I had trouble comparing them later in the algorithm, and when I did get the program to compile it still did not work as intended.
答案1
得分: 3
你对变量溢出的猜测是正确的。例如，考虑calc_decision_param_1的计算：
;d1 = y_squared - (x_squared * ry) + (1/4 * x_squared)
这个计算的结果是(50 * 50) - (40 * 40 * 50) + (40 * 40 / 4) = -77100。这已经不适合一个有符号字了，因此fistp word ptr cs:[decision_param]指令无法将默认的'IntegerIndefinite value 8000h'存储在字大小的目标中。
你应该将一些变量定义为双字整数：x_derivative、y_derivative 和 decision_param。所有其他变量将保持其当前的字大小。
检查是否 decision_param < 0 的代码应该简单地查看双字变量的符号位：
test byte ptr cs:[decision_param+3], 80hjz alternative_region_2_next
而检查是否 x_derivative < y_derivative 的代码可以使用 ficomp 来比较这些有符号双字整数。根据（冲突的）注释（;check if x_derivative < y_derivative 和 ;if it is we are done with region 1），它看起来应该是这样的：
fninitfild dword ptr cs:[x_derivative]ficomp dword ptr cs:[y_derivative]fnstsw axsahfjb calc_decision_param_2 ; done if x_derivative < y_derivativejmp region_1_loop
看起来 x_radius_squared: 和 y_radius_squared: 的功能与它们的名称所告诉我们的恰恰相反！
英文:
> I think it might be an issue with my variables(especially the derivatives and decision parameter) overflowing
Your suspicion about variables overflowing is correct.
As an example, consider the computation for calc_decision_param_1:
> ;d1 = y_squared - (x_squared * ry) + (1/4 * x_squared)
The result for this is (50 * 50) - (40 * 40 * 50) + (40 * 40 / 4) = -77100
This doesn't fit a signed word anymore and therefore the fistp word ptr cs:[decision_param] instruction can't but store the default 'IntegerIndefinite value 8000h' in the word-sized destination.
What you should do is defining some of your variables as dword integers: x_derivative, y_derivative, and decision_param. All other variables will fit their current word size.
> but I had trouble comparing them later in the algorithm
The code that checks whether decision_param < 0 should simply look at the sign bit of the dword variable:
test byte ptr cs:[decision_param+3], 80hjz alternative_region_2_next
And the code that checks whether x_derivative < y_derivative could use ficomp to compare these signed dword integers. Based on the (conflicting) comments (;check if x_derivative < y_derivative and ;if it is we are done with region 1), it would look like:
fninitfild dword ptr cs:[x_derivative]ficomp dword ptr cs:[y_derivative]fnstsw axsahfjb calc_decision_param_2 ; done if x_derivative < y_derivativejmp region_1_loopcalc_decision_param_2:
It would seem that x_radius_squared: and y_radius_squared: do exactly the opposite from what their names tell us!
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