今天水两题 = =

圆外切线

从简单的开始

最简单的两圆相切
令两圆参数分别为
{x1, y1, r1} = {0, 0, 1};
{x2, y2, r2} = {1, 2, 0.5};
用SOLVE解直线方程就可以

代码

distance[x_, y_, a_, b_] := Abs[a*x + b*y + 1]/Sqrt[a^2 + b^2];
{x1, y1, r1} = {0, 0, 1};
{x2, y2, r2} = {1, 2, 0.5};
result = Solve[
  distance[x1, y1, a, b] == r1 && distance[x2, y2, a, b] == r2, {a, 
   b}]
con = ContourPlot[(a*x + b*y + 1 /. (# & /@ result)) == 0, {x, -3, 
    4}, {y, -3, 4}];
cons = Graphics[{Circle[{x1, y1}, r1], Circle[{x2, y2}, r2]}];
Show[con, cons]

在SOLVE有多解得时候可以用/.#&/@result来对每一个结果进行求解替代

推广(雾)

多圆的情况

不总是有解

所以没有必要(这个限制的太小了)
多余的推广😄

图像插值

对一个图像插值 可以画出这种条纹字符效果

如 MOK

text = Graphics[
  Text[Style[" M O K ", FontSize -> 32, 
    FontFamily -> "Helvetica"], {0, 0}]]
textImage = 
 ImageCrop[Rasterize[Text@text, ImageSize -> 300], {300, 150}]
textImage = ColorConvert[Blur[textImage, 2], "Grayscale"]
{m, n} = Dimensions[ImageData[textImage]]
fun = Table[
   ListInterpolation[ImageData[textImage][[i, ;;]]], {i, 1, 150}];
ListPointPlot3D[
 Table[{i, k, 1 - fun[[i]][k]}, {i, 1, m, 2}, {k, 1, n, 0.1}], 
 Background -> Black, Boxed -> False, PlotStyle -> {White}, 
 ImageSize -> 800, PlotRange -> {0, 1.5}]

结果如下

调参 = = 么么哒