绘制基于椭圆sqrt的函数 [英] Draw an ellipse sqrt-based function
问题描述
我正在尝试使用基于Lua或VB的代码创建一个函数，以 绘制/绘制椭圆以及填充的椭圆.
I'm trying to make a function in Lua or VB based code to draw / plot an ellipse and also a filled ellipse.
我对此数学知识不多，可以帮些忙.
I don't have much knowledge about this math and I can use some help.
我用google搜索了有关用代码绘制椭圆的所有内容，但是我找不到一个可以将其编码到我的Lua/VB代码中的简单工作示例.
I googled everything there is to google about drawing ellipses with code but I can't find a good simple working example that i can code into my Lua / VB code.
这是我访问过的一些网站，但无法使代码正常工作或无法将代码正确转换为Lua或VB ...
here are a few websites i visited but couldn't make the code work or couldn't convert the code to Lua or VB properly...
http://groups.csail .mit.edu/graphics/classes/6.837/F98/Lecture6/circle.html
http://www.blitzbasic.com/codearcs/codearcs .php?code = 2817
https://scratch.mit.edu/projects/49873666/
http://www.sourcecodesworld.com/source/show .asp?ScriptID = 112
有人可以帮助我编写可以绘制椭圆和填充椭圆的代码吗?
Can anyone help me make code that can draw an ellipse and a filled ellipse?
这是我尝试从此处转换为Lua的一些代码:
here is some code I tried to convert to Lua from here:
https://gist.github.com/Wollw/3291916
此代码存在一些问题(缺少像素)，我认为它转换得不正确，但是我不知道该怎么做.
this code has some problems (missing pixels) and I think it's not converted properly but I don't know how to do it otherwise.
function plotEllipseRect(x0, y0, x1, y1)
-- values of diameter
a = math.abs(x1-x0)
b = math.abs(y1-y0)
b1 = 2.5
-- error increment
dx = 4*(1-a)*b*b
dy = 4*(b1+1)*a*a
-- error of 1.step
err = dx+dy+b1*a*a
-- e2 = 0
if (x0 > x1) then -- if called with swapped points
x0 = x1
x1 = x1 + a
end
if (y0 > y1) then -- .. exchange them
y0 = y1
end
-- starting pixel
y0 = y0 + (b+1)/2
y1 = y0-b1
a = a * 8*a
b1 = 8*b*b
repeat
dot(x1, y0) -- I. Quadrant
dot(x0, y0) -- II. Quadrant
dot(x0, y1) -- III. Quadrant
dot(x1, y1) -- IV. Quadrant
e2 = 2*err
if (e2 <= dy) then -- y step
y0 = y0 + 1
y1 = y1 - 1
dy = dy + a
err = err + dy
end
if (e2 >= dx or 2*err > dy) then -- x step
x0 = x0 + 1
x1 = x1 - 1
dx = dx + b1
err = err + dx
end
until (x0 >= x1)
while (y0-y1 < b) do -- too early stop of flat ellipses a=1
dot(x0-1, y0) -- -> finish tip of ellipse
y0 = y0 + 1
dot(x1+1, y0)
dot(x0-1, y1)
y1 = y1 - 1
dot(x1+1, y1)
end
end
我几乎把它装满了！ 请参阅下面这段代码中的注释，以了解问题所在...
I almost got it for the filled one! see the comments in this code below to know what the problem is...
我使用EGSL测试此Lua代码: http://www.egsl.retrogamecoding.org//pages/downloads.php
I use EGSL to test this Lua code: http://www.egsl.retrogamecoding.org//pages/downloads.php
function DrawEllipse(xc,yc,w,h)
local w2 = w * w
local h2 = h * h
local fw2 = 4 * w2
local fh2 = 4 * h2
xc = xc + w
yc = yc + h
local x = 0
local y = h
local s = 2 * h2 + w2 * (1 - h)
while h2 * x <= w2 * y do
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255)) --random color to see changes
if s >= 0 then
s = s + fw2 * (1 - y)
y = y - 1
color(255,0,255)
line(xc + x, yc + y, xc - x, yc + y)
line(xc + x, yc - y, xc - x, yc - y)
end
s = s + h2 * ((4 * x) + 6)
x = x + 1
end
x = w
y = 0
s = 2 * w2 + h2 * (1 - w)
line(xc + x, yc + y, xc - x, yc + y) --to prevent the first line to be drawn twice
redraw()
inkey()
s = s + w2 * ((4 * y) + 6)
y = y + 1
while w2 * y < h2 * (x-2) do
line(xc + x, yc + y, xc - x, yc + y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
line(xc + x, yc - y, xc - x, yc - y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
if s >= 0 then
s = s + fh2 * (1 - x)
x = x - 1
end
s = s + w2 * ((4 * y) + 6)
y = y + 1
end
dot(xc + x, yc + y)
dot(xc - x, yc + y)
redraw()
inkey()
color(int(rnd()*255),int(rnd()*255),int(rnd()*255))
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()
inkey()
end
openwindow (70,70,32,"Resize Window")
color(255,255,0)
DrawEllipse(10,10,20,20) --works perfect!
inkey()
cls()
DrawEllipse(10,10,10,20) --problems with last 2 horizontal lines between the pixels!
inkey()
cls()
DrawEllipse(10,10,20,10) --works perfect to!
closewindow()
推荐答案
好，我设法通过检查来找到填充椭圆的解决方案 如果要在椭圆的上半部分的x范围内绘制后半部分的像素.
Ok, I managed to find a solution for the filled ellipse by checking if the pixel from the second half is gonna be drawn in the x-range of the first half of the ellipse.
function drawellipse(xc, yc, w, h, dofill)
--trouble with the size, 1 pixel to large on x and y to...
w=w/2 --good solution for making it the right size?
h=h/2 --good solution for making it the right size?
local w2 = w * w
local h2 = h * h
local fw2 = 4 * w2
local fh2 = 4 * h2
-- cheat by moving xc and yc so that we can handle quadrants
xc = xc + w
yc = yc + h
-- first half
local x = 0
local y = h
local s = 2 * h2 + w2 * (1 - h)
while h2 * x <= w2 * y do
if dofill then
for i = -y , y do
color(0,255,0)
dot(xc + x, yc + i)
dot(xc - x, yc + i)
--redraw()inkey()
end
else
color(255,0,255)
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
--redraw()inkey()
end
if s >= 0 then
s =s+ fw2 * (1 - y)
y =y- 1
end
s =s+ h2 * ((4 * x) + 6)
x =x+ 1
end
color(255,0,255)
line(xc + x,0,xc - x,0)
test1 = xc + x
test2 = xc - x
print(test1 .. '/' .. test2)
redraw()inkey()
-- second half
x = w
y = 0
s = 2 * w2 + h2 * (1 - w)
while w2 * y <= h2 * x do
if dofill then
for i = -x , x do
if not(xc + i > test2 and xc + i < test1) then
color(255,255,0)
dot(xc + i, yc + y)
dot(xc + i, yc - y)
redraw()inkey()
end
end
else
color(0,255,255)
dot(xc + x, yc + y)
dot(xc - x, yc + y)
dot(xc + x, yc - y)
dot(xc - x, yc - y)
redraw()inkey()
end
if s >= 0 then
s =s+ fh2 * (1 - x)
x =x- 1
end
s =s+ w2 * ((4 * y) + 6)
y =y+ 1
end
end
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