1.碟形弹簧7 ]* e, X' n. s# A: s5 L9 H
. A7 g# ^( ]9 @/ B$ W( K9 K+ E- F# ~
圓柱坐标9 R# m& ~% L1 j% N- C! A+ p
1 v- {! p' x4 |& e$ H
r = 54 i. b3 n+ t- _'_
theta = t*36002 K1 ~* p" b* ]/ D+ z! t
z =(sin(3.5*theta-90))+24*t5 P& K4 ^+ V7 P4 _7 x* V0 D ! i& Z& s5 i% t0 V4 m
2.葉形线0 k; x6 G7 I" D7 ^2 n+ G: `9 D m# v
7 z# W0 e2 w3 L0 l
笛卡儿坐標标
" C4 `( B# l9 x# l3 P
a=10- p2 M, N5 G3 N+ ]1 o- e3 Q
x=3*a*t/(1+(t^3)), d) c: H4 g3 z+ s/ U: l
y=3*a*(t^2)/(1+(t^3)): w* m+ ]" |9 X4 A; @
& D1 M; K9 }6 c- i
3.螺旋线(Helical curve)2 ^: A+ g# E+ `; b" J) _
- B* d* @2 f; f* l+ Z4 N9 t
圆柱坐标(cylindrical)2 [* e+ t1 Z" R
4 I$ R- T: d, p" a4 e
r=t
theta=10+t*(20*360)
z=t*3
4.蝴蝶曲线
球坐标! j" i* ~4 u: D
rho = 8 * t0 x. E# ^* K7 g, D
theta = 360 * t * 4! i% d( p! b- T7 I: l$ ], @5 ~9 X
phi = -360 * t * 8
5.渐开线6 y: [! d& K, ~2 a+ m6 C) {% j
1 m( F# c8 g7 n/ N/ P. T8 }
笛卡尔坐标系0 P8 g. W' y( v4 N7 q8 O( ?
r=1
ang=360*t+ u8 x! Q) Z8 W
s=2*pi*r*t
x0=s*cos(ang)/ B# K. b1 @. [. ^# P* l
y0=s*sin(ang)5 B, e7 N" \- S' z8 N5 l
x=x0+s*sin(ang)
y=y0-s*cos(ang)9 @8 p: V, ` o+ ^3 y* t! @7 T& Y z=0 * J. e. ?: p" {" W
7 h; O. u" }* s/ J, ~6 i
6.螺旋线.
" P/ a5 R9 e' N+ J) d% Y0 g8 q
# {1 L0 [) ^7 i& e* C
笛卡儿坐标
# r8 f" t( P1 X5 r! E9 a: r+ p
x = 4 * cos ( t *(5*360))
y = 4 * sin ( t *(5*360))- y0 n, k( N/ H; M2 l% I z = 10*t
/ a p: O8 Z7 O1 g7 Z
7.对数曲线
6 L w. g# x$ v- u( U# G
/ G% h& t7 ?) G7 U s5 a2 t
笛卡尔坐标系
z=06 k( Y# {) B- l7 S: ?( O
x = 10*t
y = log(10*t+0.0001) 4 t& v d, [! b E5 X
% J: F' v" N' ?
8.球面螺旋线0 ^% p, ~' _" Z. A8 G" z
球坐标系
rho=44 I8 s3 N5 O7 |
theta=t*180/ N+ V+ z( U6 V( J
phi=t*360*20
% v4 Z& v- S7 n0 Y- G; k
8 Q- k4 r% W8 S% X- L$ d( J
9.双弧外摆线
, ?: G5 @: |! T/ y, E. H5 t4 g
卡迪尔坐标7 I" W, w' H1 ?, N6 a2 M; L
l=2.5
b=2.5
x=3*b*cos(t*360)+l*cos(3*t*360)- F! a& }5 \6 A
Y=3*b*sin(t*360)+l*sin(3*t*360)& ~% U9 ]# T4 x9 o# a0 `'Y
* `1 u. F* v# x3 C6 U A
10.星行线* W, o. V T- t8 X
卡迪尔坐标
a=5
x=a*(cos(t*360))^3
y=a*(sin(t*360))^3
9 d2 Y7 `8 e; G" W$ ~! D
11.心脏线0 j2 v7 g) J6 w- ]$ d2 F6 q0 d0 V0 k! ~
+ n8 L# [1 U# D1 J
圓柱坐标
. e- s; t8 e* t% c% d* n
a=10+ U; @; S: \. E
r=a*(1+cos(theta))1 N8 z, n' o3 T
theta=t*360
- o) j; Q- f: ^
12.圆内螺旋线
柱座标系
7 L$ z+ d% a8 U7 b+ Z% X1 \% R V
theta=t*3608 r'e5 L+ ^# L
r=10+10*sin(6*theta)/ b; n% \- m8 D5 ]4 D
z=2*sin(6*theta)
" l3 y+ T/ t. J" l" E
$ d( ]: S6 v1 N% D* w! X
13.正弦曲线
+ x6 L0 R5 i8 s3 d! W
笛卡尔坐标系# k/ o& `/ s. a# d, v* H6 {
. g/ V/ [+ n' h
x=50*t
y=10*sin(t*360); ]: ^3 i8 p'X1 W; R: {3 C1 N
z=0
( ]9 E* K! j+ k5 Q; |! e" ]0 `
14.太阳线" `1 O! I: x7 ]
柱坐标! o6 J# L: P" A/ _( K
r=1.5*cos(50*theta)+1
theta=t*360. [1 \; O- @9 ~/ `/ P+ A
z=01 u7 q; R' J4 c* `( r0 |( s
15.费马曲线(有点像螺纹线)7 Z/ W) @7 K% L9 O f7 r
数学方程:r*r = a*a*theta" A: C6 m% N8 K; n
圓柱坐标7 [& K& U( K; w+ r n0 a'~1 }0 l
方程1: theta=360*t*5% X# S1 A! | m# l/ O6 g
a=4! r, c" ~, G. l- Y
r=a*sqrt(theta*180/pi)
) H. @' l# x! k0 J9 {'O a/ @
方程2: theta=360*t*5
a=4
r=-a*sqrt(theta*180/pi)
由于Pro/e只能做连续的曲线,所以只能分两次做* ~$ V) O2 e6 N) B1 a/ _% C+ P! q
16.Talbot 曲线' |- f- `' w+ {; l) S1 Y
卡笛尔坐标
theta=t*3607 {- t" F* N/ D" o% T+ b
a=1.1
b=0.666/ w4 y5 j' I8 k" i
c=sin(theta)
f=1
x = (a*a+f*f*c*c)*cos(theta)/a; T# _4 y( n4 N& ^
y = (a*a-2*f+f*f*c*c)*sin(theta)/b
% G" w j; r5 h' f) o! ]
18.Rhodonea 曲线- v# r) p/ |$ e* k
笛卡尔坐标系
; _' Z2 h, ^/ z7 Z0 ?! \
theta=t*360*4! f& p( S1 b- i$ Y2 ]* e3 k7 e
x=25+(10-6)*cos(theta)+10*cos((10/6-1)*theta)% q9 @$ E$ w9 {5 I* H! A
y=25+(10-6)*sin(theta)-6*sin((10/6-1)*theta)
. R" M. g7 e% i4 ^+ G
19. 抛物线
笛卡儿坐标" \6 G9 H$ _& o3 w
x =(4 * t)5 ^% P1 a! @+ Z, T% U
y =(3 * t) + (5 * t ^2)
z =0
20.螺旋线
圓柱坐标
0 `; V3 C. T4 Z& n" g) X" O5 O( r
r = 5! U U5 A* U- L# x( N/ u4 }
theta = t*1800
z =(cos(theta-90))+24*t
9 Y* K! _/ E# ?4 \0 N, _
* l0 y3 s) A) m% q( B! |) g+ n
21.三叶线
圆柱坐标6 v, G3 W9 y G4 {
a=1& m7 H. }7 i1 i6 D( [( }. W
theta=t*3800 A1 B, F8 b, g7 K4 W
b=sin(theta)
r=a*cos(theta)*(4*b*b-1); S# p* T3 v% p% a- v. i* G$ X
! @2 r7 u7 s. b1 [/ O
22.外摆线0 j+ g* S: L: M' q6 q
迪卡尔坐标5 Q7 r. Q6 o7 ]5 V
theta=t*720*5T9 k+ f8 E1 c( h0 J4 b
b=8' t5 v" o7 M7 k
a=5
x=(a+b)*cos(theta)-b*cos((a/b+1)*theta)
y=(a+b)*sin(theta)-b*sin((a/b+1)*theta)( p1 e$ r. _& S1 h% X0 u) G z=08 Q6 ~5 x2 X! s# c7 G, C% z
4 m9 \ c- V4 s) B! f8 d( @
23. Lissajous 曲线( E6 f$ Z7 a! a) I
theta=t*360
a=1) ~% W, I: A. Q4 M) H5 p
b=1
c=100/ ?( e/ I" b5 a! [- `: Z
x=a*sin(n*theta+c)$ |7 x! h5 o5 r1 F) q
y=b*sin(theta)
24.长短幅圆内旋轮线* p- \7 n# S2 T
卡笛尔坐标
/ S$ v1 a# @" K8 B; a |) G
a=5& r) e. p- `1 z" H) c
b=7: t0 N: Y2 ]* `3 r. Z: t
c=2.2* H6 o" V. P8 `# J
theta=360*t*108 R6 z. f, o+ `5 {9 V
x=(a-b)*cos(theta)+c*cos((a/b-1)*theta)
y=(a-b)*sin(theta)-c*sin((a/b-1)*theta)
3 g9 ^/ I. U! A; f9 P
25.长短幅圆外旋轮线
卡笛尔坐标
theta=t*360*104 u5 w7 O% H" o$ C- c: z: F
a=5
b=3
c=5
x=(a+b)*cos(theta)-c*cos((a/b+1)*theta)
y=(a+b)*sin(theta)-c*sin((a/b+1)*theta)
1 r# |/ C' V
2 _* \) {1 y; J1 {
: f1 W/ h0 T" C2 ?
26. 三尖瓣线$ y$ H* i6 B7 s( N" T5 I
a=10$ V/ {6 v4 r, ]8 B
x = a*(2*cos(t*360)+cos(2*t*360))
y = a*(2*sin(t*360)-sin(2*t*360))
1 v, H0 W. n6 Z, O& O
! c! R/ u) [2 O/ u/ u2 Z
27.概率曲线!
笛卡儿坐标: o! q a/ Z) C; f* K/ I. n8 ~
0 k; ?% F5 H6 @4 A
x = t*10-5
y = exp(0-x^2)2 [' k: C! E5 C+ K/ m2 q1 X8 c; H; V
. c8 H4 t7 d! G6 q! i8 O9 x" B
# ~ ]1 }' l% X# ~1 N
28.箕舌线, i" I8 h1 W& ^$ X" |( Q
笛卡儿坐标系3 `2 d9 g/ z5 D) z. W2 `! _; y& w( W A ( C4 j( e- ^3 c5 F9 h+ K
x = -5 + t*109 m/ b& C( e/ z& n3 f! X
y = 8*a^3/(x^2+4*a^2)# x+ |4 n2 t ~$ x, q, [ 2 @8 b" Q7 B9 I7 p* \
: @% P" J& h5 x& M; R
29.阿基米德螺线1 s- W+ ^. t1 Y3 z+ q7 W& ?柱坐标& Z3 V' H ^2 A" b9 f
, f: X# A3 J/ n
a=100
theta = t*400
r = a*theta - w9 c$ G# Y* ]
30.对数螺线
柱坐标9 @+ N) T( `" F: ]5 D' Q
* h, i2 H4 ~& {: v/ }( h2 H
theta = t*360*2.22 ~* Q4 ^" X'{; W
a = 0.005
r = exp(a*theta)
31.蔓叶线
笛卡儿坐标系
4 E( U3 @$ I; V+ k1 a7 r& q! [/ x4 N
a=10) }) Q3 D! e% e+ M& H- l
y=t*100-509 ?& k* |" Y) F9 s4 V
solve
x^3 = y^2*(2*a-x)
for x
; y) Q4 A" t0 v. }% N/ Q'}6 u0 h& J
32.tan曲线0 n% l/ I& C" y! l( b. D
笛卡儿坐标系
x = t*8.5 -4.25
y = tan(x*20)
* k. f# m) @6 q. ~/ t5 m. E
33.双曲余弦; T/ i2 m" J; M. o/ X9 W+ D
x = 6*t-36 x& o( m1 ^4 H; Q3 u' G9 H
y = (exp(x)+exp(0-x))/2
34.双曲正弦8 C( _) c- u: q3 J8 K
; @# F4 n% ?9 Z" d
x = 6*t-3
y = (exp(x)-exp(0-x))/2
2 j) p) d) u k6 f: Y. a% R2 E4 u
; s- \- M2 M- T$ o# X H6 F
35.双曲正切& i# U. d; Z2 x" O1 ^: d- ]& g
. b6 W7 c. E+ s+ L' W- q2 S$ K
x = 6*t-3
y = (exp(x)-exp(0-x))/(exp(x)+exp(0-x))
5 Q; t" w4 o8 a3 Y8 o, P. p7 B
! j8 N$ M& B# y: S* X
36.一峰三驻点曲线
x = 3*t-1.5
y=(x^2-1)^3+1
- B% I/ P0 }. B$ ~
37.八字曲线) E' }/ L, p7 O5 B
' B; x g! k. ~2 o% L4 M N
x = 2 * cos ( t *(2*180))+ u9 I- e6 @- J' m3 i* x1 M y = 2 * sin ( t *(5*360))) a: _1 R; }9 R) M+ R
z = 0
38.螺旋曲线- f( R! x% j+ |' L
r=t*(10*180)+1
theta=10+t*(20*180)
z=t( H3 d- w6 `, X, u- ]) ^; a" `
- j! k& K% ] Z. b. M7 H; `. A
39.圆
. Y; r1 {! @) @: @# L
x = cos ( t *(5*180))
y = sin ( t *(5*180))" r6 R2 Z# f; w1 k4 O3 k, g9 I z = 0
& K( g# G; M( @
8 S7 I% C' G& ~) x
40.封闭球形环绕曲线8 @, a# u% ?/ C
, ]'O3 R" P* W2 x
rho=2* B7 H e+ A; J$ a, o
theta=360*t* L; j4 C5 |! X4 A
phi=t*360*10 " A( D. w8 D6 B7 x! _
; M3 B" L: c- l; v2 t* N" q
41.柱坐标螺旋曲线$ n% _/ ~* ~5 C! @8 | N! |
/ b& B8 \4 f% j6 T) h& f& J* o
x = 100*t * cos ( t *(5*180))/ b3 \' _8 o) D: l- g$ H( s y = 100*t * sin ( t *(5*180))
z = 02 g5 L6 s! C9 P' H0 e
42.蛇形曲线0 q7 e( e( B. Q* Y
x = 2 * cos ( (t+1) *(2*180))
y = 2 * sin ( t *(5*360))
z = t*(t+1)% c8 d0 Z% x7 T" H# i
+ @6 X' k5 \' _5 J( U e
43.8字形曲线6 X5 u$ l; ~7 o w: _'d1 {$ ?' L8 a
柱坐标
theta = t*360
r=10+(8*sin(theta))^22 P a7 x3 u: u9 l
' @, b1 W8 F! @' D! }, ]
44.椭圆曲线5 ^/ ~8 O, ?" _* g
笛卡尔坐标系% g' J) ?* K ` V' Z
a = 105 `; Z0 _' k, U
b = 20$ d, g9 G6 p! ^2 l
theta = t*360
x = a*cos(theta)
y = b*sin(theta): k! x& J, K5 M- J$ o X: e
s! x: o) T( \. U1 Y0 P/ x
45.梅花曲线
柱坐标
! k9 C+ X7 G' Y* m% T( Q4 ]
theta = t*360
r=10+(3*sin(theta*2.5))^2; V' q, E- Y2 x, f# p m
4 z
5 k% w' r. Q! [" p2 y; l
4 \# y
5 I5 M
6 J) |2 d8 h3 T
46.另一个花曲线& J* [+ r; }3 g6 U
T' |) N" D5 k( l& Z- W- t
theta = t*3601 I; l* @2 _' c2 f# h1 X8 a
r=10-(3*sin(theta*3))^2* l. k( Y4 M ]& t1 {0 F
z=4*sin(theta*3)^2
3 y& u! {5 S' m'd2 Y& _
47.改一下就成为空间感更强的花曲线了;)) B2 E: T" k* i0 | 4 B% V( F G) q2 I0 B
theta = t*3600 }& `: t$ [* P" d5 _1 f" c
r=10-(3*sin(theta*3))^22 p$ o( W'i. Q4 F6 ]7 f$ o
z=(r*sin(theta*3))^24 I; S. j0 R+ g7 h' G+ n9 b0 @* n
: ~- d# e3 C" i
48.螺旋上升的椭圆线
a = 10+ ~1 C3 X; M+ d. a* u! Q
b = 20. C" i' d- z% x8 x
theta = t*360*3, c; F5 ^0 K: l+ V7 H# r8 Z
x = a*cos(theta)
y = b*sin(theta)
z=t*12, Z7 z6 R9 Q# \- ]2 b, H
/ \% X0 q6 [0 K# ]* h
$ ]7 W4 u. d$ g3 p1 x4 D7 ^4 V
49.甚至这种螺旋花曲线- }3 c- m8 O9 g+ S) \
; l* k2 p: Y$ i, Q+ h! x: B; B" O' m
theta = t*360*4
r=10+(3*sin(theta*2.5))^2! p# I9 J% |8 i8 U5 U
z = t*16
" f; m# A1 g B) t. C0 x
50 鼓形线
笛卡尔方程0 [+ Y% i; `9 j
1 i: y3 [9 X3 L: r
r=5+3.3*sin(t*180)+t
theta=t*360*103 C9 p! X \4 C; b
z=t*100 c: a- F+ _4 i# V
51 长命锁曲线
笛卡尔方程:
: V5 [! _9 z+ t% g
a=1*t*359.59 O& r, Q7 L$ L6 w2 X
b=q2*t*360' g8 n9 T( ~- ]% o
c=q3*t*360: i) K* P8 c3 [) S+ K
rr1=w1
rr2=w24 h/ G2 S; W$ |) h! J& l
rr3=w3. h% Y'D A4 D
x=rr1*cos(a)+rr2*cos(b)+rr3*cos(c)1 k& M7 G0 {2 @) V. ? y=rr1*sin(a)+rr2*sin(b)+rr3*sin(c)
. \' t5 x; S+ X
7 [0 d) d" X7 }* J. @
52 簪形线- l6 c, {( j3 e
球坐标4 y'M9 u! [" W& Y: ^( e6 y! f
rho=200*t B5 Z: y3 g% b8 N
theta=900*t7 V* v$ |* j) r5 c1 J
phi=t*90*107 Z% h& k+ q) P1 f" x
' W" I; x8 S* ]
53.螺旋上升曲线: \& e; ~6 p% j+ |$ }! J- k
( a3 d; |* e; V* u% G6 D8 W
r=t^10
theta=t^3*360*6*3+t^3*360*3*36 @% {0 p+ N- l6 b
z=t^3*(t+1)
0 E* C" c( Q$ S1 ?5 o; O
. y5 |9 O: X9 r, @
54.蘑菇曲线' z- n; \: _6 D8 I# Y/ X7 a
球坐标- E/ S$ l9 Q/ A6 ?' \6 L
rho=t^3+t*(t+1). e( j+ F/ a( G$ O# @5 O# ^6 o. [# W
theta=t*360
phi=t^2*360*20*20/ |& @! G9 I3 M5 D; J
6 R5 B+ H, E- l" q: D( s" e
3 W e" ^0 g" Q) K
55. 8字曲线
! E. k& P5 P0 q- D: V9 r, e
a=1+ V0 ^! }& ?% M9 i6 ^( N7 L* I
b=1
x=3*b*cos(t*360)+a*cos(3*t*360)
Y=b*sin(t*360)+a*sin(3*t*360). }5 N8 \) j9 r* _# u* I, c& p # V2 k" d ^" W- i0 Q5 C
56.梅花曲线4 D+ @$ ?4 B$ ^6 j# r. ~! c
. J% U9 Z7 [5 I( ]
theta=t*360) D# z0 s/ `* w4 W6 R7 K
r=100+50*cos(5*theta)/ T, j: A0 U9 P# ~) g) t; @
z=2*cos(5*theta)
1 q* a" q5 a. A) N
2 Y'w" n9 g6 j
57.桃形曲线$ N) q8 J2 u. w* l* w5 o% U0 d
, r4 O, j% @+ [1 x& o7 H6 L
rho=t^3+t*(t+1)9 }& x' P# M0 P3 ?$ q) l% X* Z
theta=t*360+ T. J( D, I v
phi=t^2*360*10*10# C W, I) T7 {; v't
7 n; |! n9 a" ?% U" X% ?
# O/ z0 W" ]! k& \: m: ^7 V# }
58.碟形弹簧
圓柱坐
7 T6 w/ g: R) e& _/ l
r = 5
theta = t*3600, C9 w3 u0 N% p5 H& T- q* z0 |
z =(sin(3.5*theta-90))+24
: |/ d6 v; d( t- C: o
59 环形二次曲线_! ]# i+ I% \* W, x% w
笛卡儿方程:
' ^" N9 V6 x, E' `, w6 v2 _4 z! W
x=50*cos(t*360)( b2 ~, e! `- W* E, A) F
y=50*sin(t*360), ^2 |B# {) ]. C* V
z=10*cos(t*360*8)8 N* B7 O( t3 A0 e
f% S/ H! b& w0 M! ^
* K; Q) P1 }3 i2 z, v" l# K" s
60 蝶线/ s4 [' ?) [ s6 o; r- P# {
球坐标:4 o0 @% G1 c4 ?* P2 M# } x1 a
6 g# d1 D" [; J* k
rho=4*sin(t*360)+6*cos(t*360^2)" V1 M2 {( s S
theta=t*3609 ?/ f( Y, I) }! k" Y3 l$ J
phi=log(1+t*360)*t*360
7 k- N8 }/ o4 M3 |" W
61.正弦周弹簧: S. y2 S" F5 y2 T' f
笛卡尔:, Y2 i+ J2 t6 x$ X
ang1=t*360; u$ r& ]# B* i& @+ M
ang2=t*360*20
x=ang1*2*pi/360
y=sin(ang1)*5+cos(ang2)- H0 W5 f5 q: L: Z, e. G) y5 f
z=sin(ang2)$ s2 q0 g7 m6 X A0 k'r% Y
- F$ w2 V d6 I8 `
* C; b+ j8 c" s& a
62.环形螺旋线
笛卡尔:! @$ V- }$ z" |5 k/ w* J5 ^
# t! K9 a3 Y1 R( g" ]/ }
x=(50+10*sin(t*360*15))*cos(t*360)( m$ x7 j5 h) o. c! ~ y=(50+10*sin(t*360*15))*sin(t*360)- G7 L, Z5 m/ B6 j6 d6 T
z=10*cos(t*360*5)& c0 \" ?4 z; v% M. B. T, m
3 x7 {6 _6 Z8 t- i% |7 Y! I
63.内接弹簧0 m r7 d) q5 m
笛卡尔:
$ t' v! F9 n, s7 m+ B3 F) ~6 P
x=2*cos(t*360*10)+cos(t*180*10); g- d& A% x2 X, d y=2*sin(t*360*10)+sin(t*180*10), n* V+ x0 h4 v! e z=t*6
, q; q5 s$ }; T$ Y& d
64.多变内接式弹簧
笛卡尔:: _5 k6 _: W+ F# I4 Y
& b" q& ^1 k5 J6 C3 V! z! [
x=3*cos(t*360*8)-1.5*cos(t*480*8)
y=3*sin(t*360*8)-1.5*sin(t*480*8)
z=t*88 S9 s; y" B: G- Q) ^+ p/ m T4 i
65.柱面正弦波线
柱坐标
! T9 i8 p* l( }( D
r=302 }8 T& E- H2 u
theta=t*360
z=5*sin(5*theta-90)+ U( M1 z: {6 ?& K) ?% ^9 K. k
; v9 H4 g+ Y% ^9 O
66.漩涡线* f# y G, A! I'o" [5 M; @! G7 @
球坐标:% R, v: l5 T) W2 F5 u
rho=t*20^2w. I. B0 I'o
theta=t*log(30)*60
phi=t*7200- t; s3 k5 s( ~: a1 o
# G e% E2 ?6 v0 L7 z5 z
67. 手把曲线
笛卡尔:7 l+ Q, z. X+ X* I/ y; E5 F& L
9 c j5 Z# i; a8 O! `
thta0=t*360
thta1=t*360*6
r0=400
r1=40
r=r0+r1*cos(thta1)
x=r*cos(thta0)6 z. r# y7 x, M% i" V5 N
y=r1*sin(thta1)
z=00 H2 B D' R+ T4 k
68.篮子
圆柱坐标
r=5+0.3*sin(t*180)+t
theta=t*360*30
z=t*5
2 T* u1 r) Z4 H% {
69. 圆柱齿轮齿廓的渐开线方程:1 @& q4 x& h3 `0 |/ f4 A
笛卡尔坐标
afa=60*t0 Z/ U# |! u1 z
x=10*cos(afa)+pi*10*afa/180*sin(afa)
x=10*sin(afa)-pi*10*afa/180*cos(afa)
z=0
注:afa为压力角,取值范围是0到60,10为基圆半径。
70.对数螺旋曲线
柱坐标:* Q6 @/ H3 |. e
r=sqrt(theta)
theta=t*360*308 |- r/ y% B' d( x" F9 X
z=0
' k& h. D: y" w n' t
71. 罩形线
球坐标:! c, U7 t. v5 M9 `) B/ a
rho=42 o$ Q. Y0 U9 z: T8 G/ ?1 X
theta=t*60
phi=t*360*102 n0 L/ ]% m3 ~! K& B
t0 N( @3 j0 T5 _+ L* {1 f
; E5 h9 c% ~, L$ I8 Y) ~6 L
72. 向日葵线
笛卡尔:M& Z1 i0 M* I, Q& V0 L
5 ^* Q* d
6 z" q, i: b
theta=t*360
r=30+10*sin(theta*30)
z=0% j. ^$ Y( T5 R. s8 E3 h
73. 太阳线! j/ K. y6 V* H
笛卡尔:
r=1.5*cos(50*theta)+11 G. Z7 H0 K2 w8 |! V
theta=t*3600 k+ @. R- m) P6 U0 q/ z3 V, d" M
z=0* \9 K'`+ b% d# h
74 塔形螺旋线
笛卡尔:
r=t*80+500 ?. B) N% Q ]3 `
theta=t*360*10. r$ j6 F1 t8 E5 ~+ Z5 E
z=t*80# a/ D3 z$ c. Q3 D) L
5 F
6 V' R F K2 e0 k4 P1 y. D0 j8 _
75 花瓣线
球坐标:
rho=t*20+ z5 k* ~4 X4 _4 Y) }. Y
theta=t*360*90
phi=t*360*10. n& [; U6 K* k. C, R4 J0 U+ n
76 双元宝线! Q y3 ~9 e$ P" j' z'~6 D, c& N
笛卡尔:
, J e# i( G4 ~( B$ x0 m
r=sin(t*360*10)+30- x. v- M7 C+ Y+ c# ]3 V( g5 W+ f theta=sin(t*360*15)
z=sin(t*3)
4 b4 F* n1 y( y7 m* |7 c* ?
' s1 \+ h, y9 F, ^5 F'e3 D. S: W0 |
77 阿基米德螺线的变形: S! H% g: {' k8 L1 p' U9 }3 t 柱坐标
2 J; c+ V s5 s( `7 h+ r$ A R9 p
theta=360*2*(t-0.5); e5 ~'@& B: N4 g( V
r=10*theta
z=0
1 n+ @+ q9 l- l5 I) I
78 改过来的渐开线方程5 D0 ~5 d% V6 f1 |. E8 R# S
r=20
ang = t*360* ~+ ~3 M$ a- l
x=r*cos(ang)+2*pi*r*t*sin(ang), V1 x* q; u% K+ X7 c3 A& c8 \'B
y=r*sin(ang)-2*pi*r*t*cos(ang)
z=00 R& V6 H4 [9 `. W
前面的方程是这样的:(对比研究一下两者有什么不同)9 E% q; y I& g' O9 ?0 F5 q 采用笛卡尔坐标系
r=1: f1 @$ s; i" H( u$ `. n! \
ang=360*t; [. t3 ^; @/ u1 I2 F
s=2*pi*r*t
x0=s*cos(ang)
y0=s*sin(ang)/ |% m, R" r% \2 [8 R
x=x0+s*sin(ang)8 N& G" Q' T4 I0 M ?1 W# a
y=y0-s*cos(ang)5 ]( M, x6 ], l1 B2 f
z=0
3 C, n9 a! n* i9 S& N
79 双鱼曲线6 E" ^2 M0 C3 z9 n* V) O2 d
球坐标系
% }0 H7 p'u1 v ^- M! Y! U, i
rho=30+10*sin(t*360*10)! k5 ]" a6 h. d" [2 \
theta=t*180*cos(t*360*10)% `; v; A'K) t& y$ f& o( v8 ^
phi=t*360*30! h- f" {0 T9 I/ j8 H7 f4 A# Q
80 蝴蝶结曲线$ G8 z1 E ^- L8 W Q8 P% ~: o
迪卡尔坐标
x=200*t*sin(t*3600)3 p( z- n* X1 o3 z4 Q
y=250*t*cos(t*3600)! H% h. _# i5 n* L W, _; r
z=300*t*sin(t*1800): M; f. r# s. g; x& j- w* ]
81 ”两相望“曲线/ p- O3 x% e( A9 r, E; V. }: p
球坐标系
$ c, Q) n% Y2 e7 \- O6 X
rho=30
theta=t*360*cos(t*360*20)
phi=t*360*20
% L% X3 w% W7 Z# C2 W
82 小蜜蜂+ C b! z& h- A1 Q& V2 C/ c
笛卡尔坐标系:
x=cos(t*360)+cos(3*t*360)
Y=sin(t*360)+sin(5*t*360)
83 弯月
x=cos(t*360)+cos(2*t*360)9 ^'b7 s. `: x) f( ]! a Y=sin(t*360)*2+sin(t*360)*2
84 热带鱼7 d* c- _; y* f+ @' H; b
a=5
x=(a*(cos(t*360*3))^4)*t- u( u* ~4 Y) k
y=(a*(sin(t*360*3))^4)*t0 D8 x( S7 d: N; g; W
85 燕尾剪i- B1 v. p! ?
+ J F- _% ~4 T
x=3*cos(t*360*4)+ e. N'Y6 ] I3 Z
y=3*sin(t*360*3)
z=t; @- a2 ]7 E' m" T& E* h$ S
0 P- w' k: Y! a {+ ]
; p1 p$ P, t" \# f! E2 W
86 天蚕丝$ ^( o0 O& x$ y% w1 ?- l
柱坐标
5 A0 l: v! d3 M4 Q; ^
theta=t*3600. }1 p* c7 u5 O5 k
r=(cos(360*t*20)*.5*t+1)*t
4 ]% a, d& x" L9 T
. h& ]$ ]) U# R0 b b0 ]
87 心电图
圆柱坐标系:
7 o1 S* H8 D! n1 z" v. @1 j5 s( w, _
r=sin(t*360*2)+.23 w+ `+ \- L% k Q
theta=10+t*(6*360)2 g2 Y) E! o4 l7 J0 z7 e) |0 r z=t*3
% `* F0 D: l+ I: h& |, w1 K
88 变化后的星形线5 \" N$ Y; T# A* Q/ H
迪卡尔坐标系% i2 O: c! o: A1 ^3 T: K. |$ X
theta=t*3608 p, O1 _'Y+ O2 `6 r, E, V
x=10*cos(theta)^3' x, d: O i6 G0 M
y=10*sin(theta)^36 d. H" `( v% X O; {" q0 x& H+ ~! C z=cos(theta)
89 小白兔/ ^5 y% y P6 ~& j- M
) \3 B9 w) n% U& I; d; b/ o" ~9 D
theta=t*360-90
r=cos(360*(t/(1+t^(6.5)))*6*t)*3.5+5
90 大家好) F" l/ h; j. d* S4 i2 L4 C5 @
柱坐标2 t% a1 B B, S+ v, J7 a
theta=t*360+180
r=cos(360*t^3*6)*2+5
91 蛇形线$ Q& P4 T3 p- z0 B5 G
笛卡尔坐标系:
( N: g# B) a1 \3 K1 Q" j {. J* B" r
x=2*cos(t*360*3)*t# c/ g ]: M. v$ j2 ]
y=2*sin(t*360*3)*t( j# B( o. d* j7 Q# K7 [+ ?
z=(sqrt(sqrt(sqrt(t))))^3*5
! L y b% p9 A. V
& T+ g$ o6 i6 V* D5 l- d) L
92 五环
柱坐标:
theta=t*360*4' V! _* d2 R8 Z* `" d) v* B( T
r=cos(t*360*5)+1
3 K& [
4 b: m3 P
93 蜘蛛网
柱坐标:M C2 a2 \'x4 V' o7 }4 i2 K
theta=t*360*52 j: Y `/ `# o( j4 X: }. Z. `
r=t*sin(t*360*25)*5+8
8 l$ }$ l3 u4 H l
94 次声波
笛卡尔:
x=t*55 I' k, `& Z9 F# v
y=t*cos(t*360*8)
9 p# \( [' i+ z- B' ?+ A$ i. D
95 十字渐开线; ~6 V) E8 y' \- \3 p: f
柱坐标:2 M# Y8 L- L$ {8 W
3 g# a/ T& \" p3 m
theta=t*360*4
r=(cos(t*360*16)*0.5*t+1)*t) e" }* j% ]; T* @
. _/ ^+ O" v: l- `1 V
, e- z; D, z$ i- { C3 y
96 内五环) I# ^8 i9 R! O/ u1 V7 H5 L
笛卡尔0 K- a2 \7 z$ e/ F# Z" N- J
' ~& [5 ?. S6 V2 N( R0 O+ o
theta=t*360*4
x=2+(10-5)*cos(theta)+6*cos((10/6-1)*theta)
y=2+(10-5)*sin(theta)-6*sin((10/6-1)*theta): H) L, \5 M: J0 l; H* c5 e+ }
1 e4 E$ [5 ~& s
97 蜗轨线" Z% E5 W5 T* B0 q' S0 T
柱坐标;
theta=t*360*2( m6 M5 ~5 w9 C8 g) g4 @! ^5 f) M
r=cos(t*360*30)*t*0.5+t*2* g; s* _8 |. N' K4 l
]% v1 o# d. |/ ^% S2 |$ d# a8 z
98.鼓鼓形线9 q" U, A# e" v) }( V% x
r=6*sin(t*360)+t% L; J7 v: f9 ?2 } i) g
theta=t*360*20
z=t*202 t3 t. {% p. f2 F5 ^
( t, M* }! S- ?: |Z
1 J6 c+ h5 z m3 Y: T
99.笛卡尔坐标系的圆内螺旋线- \'z" F9 w# f
0 [ E2 i. O2 ?8 i e0 g
a=5
b=3! e2 d% g& N# _6 T& V5 d$ w' ^- w3 Y
x=(a-b)*cos(t*360*180/pi)+b*cos((a/b -1)*t*360*180/pi)
y=(a-b)* sin(t*360*180/pi)-b*sin((a/b -1)*t*360*180/pi): R% ~) y' O* \8 B+ o z=0! a7 c; K5 D b/ x# E8 j
( s, M; E1 {7 j$ x# f0 p
0 o# u9 F- A4 U" F* K
100.肾形线" e) `& S9 k% ?, `
柱坐标系
a=2) l$ ?+ A! W% o c9 P% f7 z
theta=t*360*180/pi3 e' S- C6 s$ A) {: w) H
r=a*(1+2*sin(theta/2))
z=07 o4 a) R3 ~' B$ X& G4 C3 s8 ~7 u5 r
101.花形% I! l Y' \5 a: ?
柱坐标
" s2 c9 U( F! @
theta = t*3600 G" K6 H& u- k. Y4 H: u
r=5-(3*sin(theta*3))^2# T# J! I' o) E$ y) Y7 y# i! `
z=(r*sin(theta*3))^2
the=t*360
r=10+(3*sin(the*2.5))^2
z=5*sin(6*the)2 S4 j4 V( k! I4 D$ k) I
8 S# V# |( K+ V$ {'? f
102.一朵小花
圆柱坐标系
theta= -t*360+180! F, K1 L1 g4 O- p0 {: p. _
r=cos(360*t/(1+t^8)*7)*3+6
103. 人民币
, G1 R/ N$ H; o7 m' ]9 Z
theta=-t*360+180+ V5 W$ s3 i; k2 }; m
r=cos(360*(t/(1+t^6))*6)*3+54 W0 n+ B' ~. m: X7 R % P7 w2 ]+ f' t' G& I0 S! M
' e1 u7 K8 ]' k) o
104. 天蚕丝
theta=t*3600* r [- s3 L1 W4 l
r=(cos(360*t*20)*.5*t+1)*t
- M( X7 ]' A5 S$ X. V2 y
105. 红十字
r=cos(360*t*4)*.5+19 ] ^# M, A# l& g% Q5 U o theta=t*360+90
3 C, t: G( B. u% @+ _ Q7 B! n
106. 波浪花带