ruhuasiyu
本帖最后由 ruhuasiyu 于 2016-8-17 20:24 编辑

上一次发了一个画Bezier曲线的帖子，那个方法可以画任意由多项式函数给出的曲线。帖子地址为
http://www.mcbbs.net/thread-620979-1-1.html
而且在帖子结尾加了一个在线生成OOC的工具，可以方便地画二次Bezier曲线。例如


然而却不能处理三角函数值。


在这个帖子中我将尝试画著名的屁股曲线(心形线)
ρ=1+cos t


整体结构如下图，左上方为位移用的命令，右下方是初始化，中间为计算坐标用。


原理

我们将利用近似公式
sin x=x-x^3/6+x^5/120
cos x=1-x^2/2+x^4/24

实际计算时采用下式
10000*sin (pi/2 * t/N)=(157080*t/N-64596*t/N*t/N+7969*t/N*t/N*t/N)/10
10000*cos (pi/2 * t/N)=(100000-123370*t/N*t/N+25367*t/N*t/N*t/N*t/N)/10
最后将结果的整数部分保存在 #sint 和 #cost 中(注意会差一些比例)，然后计算
#x=ρ cost=(1+#cost)#cost
#z=ρ sint=(1+#cost)#sint

命令

首先在记分板temp中引入下述变量

shi                10
yiwan            10000
abc                临时变量
t                    角度
N                   均分次数
sint                正弦
cost               余弦
x                   x坐标
y                   y坐标
z                   z坐标


初始化
设置各变量的值和循环次数
  1. scoreboard players set #rat temp 1000
  2. scoreboard players set #N temp 20
  3. scoreboard players set #t temp 0
  4. scoreboard players set #sint temp 0
  5. scoreboard players set #cost temp 0
  6. scoreboard players set #x temp 0
  7. scoreboard players set #y temp 0
  8. scoreboard players set #z temp 0
  9. summon Snowball ~ ~ ~ {CustomName:"a",NoGravity:1}
复制代码






位移
执行位移共 5*3部分，每部分检测#x,#y,#z 是否落于1-9,10-99,100-999,1000-9999,10000-10000000内，然后进行移动。
  1. scoreboard players test #x temp 10000 100000000
  2. execute @e[name=a] ~ ~ ~ tp @e[name=a] ~10 ~ ~
  3. scoreboard players remove #x temp 10000
复制代码



计算坐标
计算过程命令如下，依次为“检测与召唤”、“计算sint”（橙色），“计算cost”（紫色），“计算ρ，x，y”（黄色）



  1. scoreboard players test #t temp 0 19
  2. scoreboard players test #x temp 0 0
  3. scoreboard players test #y temp 0 0
  4. scoreboard players test #z temp 0 0
  5. 比较器
  6. entitydata @e[type=Snowball] {CustomName:""}
  7. summon Snowball ~ ~ ~ {CustomName:"a",NoGravity:1}
  8. scoreboard players add #t temp 1

  10. scoreboard players set #a temp 157080
  11. scoreboard players operation #a temp *= #t temp
  12. scoreboard players operation #a temp /= #N temp
  13. scoreboard players operation #b temp = #a temp
  14. scoreboard players set #a temp -64596
  15. scoreboard players operation #a temp *= #t temp
  16. scoreboard players operation #a temp /= #N temp
  17. scoreboard players operation #a temp *= #t temp
  18. scoreboard players operation #a temp /= #N temp
  19. scoreboard players operation #a temp *= #t temp
  20. scoreboard players operation #a temp /= #N temp
  21. scoreboard players operation #b temp += #a temp
  22. scoreboard players set #a temp 7969
  23. scoreboard players operation #a temp *= #t temp
  24. scoreboard players operation #a temp /= #N temp
  25. scoreboard players operation #a temp *= #t temp
  26. scoreboard players operation #a temp /= #N temp
  27. scoreboard players operation #a temp *= #t temp
  28. scoreboard players operation #a temp /= #N temp
  29. scoreboard players operation #a temp *= #t temp
  30. scoreboard players operation #a temp /= #N temp
  31. scoreboard players operation #a temp *= #t temp
  32. scoreboard players operation #a temp /= #N temp
  33. scoreboard players operation #b temp += #a temp
  34. scoreboard players operation #sint temp = #b temp

  36. scoreboard players set #b temp 100000
  37. scoreboard players set #a temp -123370
  38. scoreboard players operation #a temp *= #t temp
  39. scoreboard players operation #a temp /= #N temp
  40. scoreboard players operation #a temp *= #t temp
  41. scoreboard players operation #a temp /= #N temp
  42. scoreboard players operation #b temp += #a temp
  43. scoreboard players set #a temp 25367
  44. scoreboard players operation #a temp *= #t temp
  45. scoreboard players operation #a temp /= #N temp
  46. scoreboard players operation #a temp *= #t temp
  47. scoreboard players operation #a temp /= #N temp
  48. scoreboard players operation #a temp *= #t temp
  49. scoreboard players operation #a temp /= #N temp
  50. scoreboard players operation #a temp *= #t temp
  51. scoreboard players operation #a temp /= #N temp
  52. scoreboard players operation #b temp += #a temp
  53. scoreboard players operation #cost temp = #b temp
  54. scoreboard players operation #sint temp /= #shi temp
  55. scoreboard players operation #cost temp /= #shi temp

  57. scoreboard players set #rho temp 100000
  58. scoreboard players operation #rho temp += #cost temp
  59. scoreboard players operation #cost temp *= #rho temp
  60. scoreboard players operation #cost temp /= #yiwan temp
  61. scoreboard players operation #sint temp *= #rho temp
  62. scoreboard players operation #sint temp /= #yiwan temp
  63. scoreboard players operation #x temp = #cost temp
  64. scoreboard players operation #z temp = #sint temp
复制代码




结果示例

下图是屁股线的1/4部分(第一象限，方向和上面的图相反)


将执行位移的命令添加上适当的符号，将函数由1+cos t 变成1-cos t，可以得到其他象限的图像。


利用此种方法可以处理任意由三角函数和初等运算组成极坐标的曲线，诸如

圆








ρ=sin3t



等等。不过现在只完成了第一象限的绘制，其它三个象限还没完成。另外精度上还可以略作提高，不过由于记分板数值的限制，还不能做到无限精确。


















儚无水木
数学渣膜拜中……
（我第一次看到心形线被叫成屁股曲线）
lcplcplcp
好强。。不太明白在说什么
火星浮云
膜拜大神，不过恕我冒昧，运用MC计算出这些曲线的实际意义不大……
小烦
daolao……
ruhuasiyu
火星浮云 发表于 2016-8-17 19:34
膜拜大神，不过恕我冒昧，运用MC计算出这些曲线的实际意义不大……

可以在建筑中作出各种曲线
乙烯_中国
可以，你摸到门路了，可以来和我学做菜了。
开玩笑的，虽然说这计分板的使用还是想吐点槽的，但是整体上使用的很不错，包括对计算结果的取舍。
Zevn
话说这样很卡吗？
ruhuasiyu
Zevn 发表于 2016-8-22 00:55
话说这样很卡吗？

运行的时候因为位移花的时间比较长，略微有点卡，不是非常卡
Command_Zeus
明明是笛卡尔的最后一封情书好不好
Ph-苯
准初三路过……
机器人WBW
well三角函数
不是精确数值强迫症表示不爽但是能算出来也是非常nice了
嗯已收藏
leich123
真心不错{:10_512:}
Zevn
。。第一次看的时候还不是很懂，这次看算是懂了大概的原理。
1902478744
咸鱼的我...看不懂
pineapple_
sin x=x-x^3/6+x^5/120
cos x=1-x^2/2+x^4/24

这个帖子我可能只学到了这个
a1597251152
MCBBS有你更精彩~