公式集合（Formula set）

公式集合（Formula set） 公式集合(Formula set) sd49 = 7 + evalgraph(“0”，国防部(trajpar * 250,10))* 1.5 sd48 = 7 + evalgraph(“0”，国防部(trajpar * 250 + 10))* 1.5 mod()函数 在进行讲解前，我们需要先了解一个将在这个过程扮演重要角色的函数:mod()。mod()函数是Pro/ENGINEER中用于数学求余的函数，下面就是一些求余的结果: MOD(10,3)= 1 MOD(10.5,3)= 1.5 MOD(10.5,3.1)= 1.2 „ 因为我们要实现循环利用图形，那么在我们的可变扫描过程中，我们必须有方法在某个值后归零然后重新计算图形对应的值，很显然mod()函数是非常恰当的实现方式。有关图形循环利用的概念，christ000版主提出这个方法时他实现的方法是用地板函数来进行计算余数，其实两者方式结果都是一样的，不过mod()函数的方式更直观和直接。假设我们的图形X宽度为10，而我们要在可变扫描过程中循环利用5次的话，那么我们就可以使用mod()函数来进行如下的关系编写: SD # = evalgraph(“图”，MOD(50×trajpar，10))或 SD # = evalgraph(“图”，50×trajpar地板(5×trajpar)* 10) 很显然第一种方式更为直观容易理解，我们简单说明一下它的意义，在我们的整个可变扫描过程中，trajpar是从0到1变化，所有50×trajpar的变化就是0到50，MOD(50×trajpar，10)的意思就是这0到50的变化要对10进行求余，换句话说，当变化到10的倍数的时候我们的mod()函数值就会归0，从而实现图形的循环利用，floor()函数的基本方式也是一样 阿基米德螺旋线公式圆拄系 θ,t * 360×5 r = 2.5 + 4 * t * 5 Z = 0 齿轮，基圆直径= m×Z×COS压力角 DF ] 1 = Mn?Z1,2?(汉，CON,XN1)?锰 α= 20压力角是2 M = 2模数 Z = 30齿数 C = 0.25 哈= 1 db = Z *余弦(余弦) R =(db / 2)/ COS(t * 50) θ=(180 /π)*滩(T 50)T * 50-0.3是齿宽度- 0.3可以调 Z = 0 sd9 = evalgraph(“HH”，trajpar×10) 如果trajpar >。9 0.6-cos SD6 =((trajpar-0.9)×900)0.5×0.6 ^ 其他的 SD6 = 0 如果是语句结束 如果是假设和如果别的是其他的 铁丝网公式 SD3 = sin(360×trajpar×20)×1 SD4 = sin(180×trajpar×20)×6 圆拄殿 如果D1,5 D0 = 1 其他(否则) D0 = 2 如果(结束如果语句) 对在X-Y平面的一个圆，中心在圆点 半径= 4，参数方程将是 x,4×余弦(t * 3600) y,4,,(t * 360) Z = 0 正弦曲线 笛卡尔坐标系 方程:x = 50 * T y,10,,(t * 360) Z = 0 螺旋线。 笛卡儿坐标 方程:x = 4×cos(T *(5 * 360)) y,4 *(t *(5×360)) z,10×t 对球坐标系，输入参数方程 根据，(将从0变到1)对ρ，θ和 例如:对在X-Y平面的一个圆，中心在圆点 半径= 4，参数方程将是 ρ= θ= 9 φ= t * 36 正弦曲线 笛卡尔坐标系 方程:x = 50 * T y,10,,(t * 360) Z = 0 螺旋线。 笛卡儿坐标 方程:x = 4×cos(T *(5 * 360)) y,4 *(t *(5×360)) z,10×t 内五环 笛卡尔 θ,t * 360×4 x = 2 +(10-5)* cos(θ)+ 6 * cos((10,6-1)×θ Y = 2 +(10-5)×sin(θ)- 6 *罪((10,6-1)×θ) Trajectory of cochlea Cylindrical coordinate; Theta=t*360*2 R=cos (t*360*30) *t*0.5+t*2 Natural silk Theta=t*3600 R= (COS (360*t*20) *.5*t+1) *t electrocardiogram Cylindrical coordinate system: R=sin (t*360*2) +.2 Theta=10+t* (6*360) Z=t*3 Little white rabbit Theta=t*360-90 R=cos (360* (t/ (1+t^ (6.5))) *6*t) *3.5+5 Theta=t*360+180 R=cos (360*t^3*6) *2+5 Serpentine line Descartes coordinate system: X=2*cos (t*360*3) *t Y=2*sin (t*360*3) *t Z= (sqrt (sqrt (sqrt (T))) ^3*5 Five Cylindrical coordinate: Theta=t*360*4 R=cos (t*360*5) +1 Spider web Cylindrical coordinate: Theta=t*360*5 R=t*sin (t*360*25) *5+8 Infrasonic wave Descartes: X=t*5 Y=t*cos (t*360*8) Cross involute Cylindrical coordinate: Theta=t*360*4 R= (COS (t*360*16) *0.5*t+1) *t Sine spring Descartes: Ang1=t*360 Ang2=t*360*20 X=ang1*2*pi/360 Y=sin (Ang1) *5+cos (Ang2) Z=sin (Ang2) Ring helix X= (50+10*sin (t*360*15)) *cos (t*360) Y= (50+10*sin (t*360*15)) *sin (t*360) Z=10*cos (t*360*5) Inscribed spring X=2*cos (t*360*10) +cos (t*180*10) Y=2*sin (t*360*10) +sin (t*180*10) Z=t*6 Variable internal spring 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*8 Cylindrical sinusoidal line Cylindrical coordinate: equation R=30 Theta=t*360 Z=5*sin (5*theta-90) Spherical coordinate: Rho=t*20^2 Theta=t*log (30) *60 Phi=t*7200 Handle curve Thta0=t*360 Thta1=t*360*6 R0=400 R1=40 R=r0+r1*cos (thta1) X=r*cos (thta0) Y=r1*sin (thta1) Z=0 Basket Cylindrical coordinates R=5+0.3*sin (t*180) +t Theta=t*360*30 Z=t*5 Involute equation of cylindrical gear profile: Afa=60*t X=10*cos (AFA) +pi*10*afa/180*sin (AFA) X=10*sin (AFA) -pi*10*afa/180*cos (AFA) Z=0 Note: AFA is the pressure angle, the range is from 0 to 60, and 10 is the base circle radius. Logarithmic spiral curve Cylindrical coordinate: R=sqrt (theta) Theta=t*360*30 Z=0 Hood line Spherical coordinate: Rho=4 Theta=t*60 Phi=t*360*10 Sunflower thread Theta=t*360 R=30+10*sin (theta*30) Z=0 Solar rays R=1.5*cos (50*theta) +1 Theta=t*360 Z=0 Spiral tower R=t*80+50 Theta=t*360*10 Z=t*80 Petal line Spherical coordinate: Rho=t*20 Theta=t*360*90 Phi=t*360*10 Double ingot line R=sin (t*360*10) +30 Theta=sin (t*360*15) Z=sin (t*3) Deformation of Archimedes spiral Theta=360*2* (t-0.5) R=10*theta Z=0 Modified involute equation R=20 Ang = t*360 X=r*cos (ANG) +2*pi*r*t*sin (ANG) Y=r*sin (ANG) -2*pi*r*t*cos (ANG) Z=0 Pisces curve Spherical coordinate system Rho=30+10*sin (t*360*10) Theta=t*180*cos (t*360*10) Phi=t*360*30 Bow tie curve X=200*t*sin (t*3600) Y=250*t*cos (t*3600) Z=300*t*sin (t*1800) "Two faces" curve Spherical coordinate system Rho=30 Theta=t*360*cos (t*360*20) Phi=t*360*20 Little bee Descartes coordinate system: X=cos (t*360) +cos (3*t*360) Y=sin (t*360) +sin (5*t*360) Crescent X=cos (t*360) +cos (2*t*360) Y=sin (t*360) *2+sin (t*360) *2 Tropical fish A=5 X= (a* (COS (t*360*3)) ^4) *t Y= (a* (sin (t*360*3)) ^4) *t One peak and three stationary point curves X = 3*t-1.5 Y= (x^2-1) ^3+1 [express download,]36.jpg: Splay curve X = 2 * cos (t * (2*180)) Y = 2 * sin (t * (5*360)) Z = 0 Spiral curve R=t* (10*180) +1 Theta=10+t* (20*180) Z=t circular X = cos (t * (5*180)) Y = sin (t * (5*180)) Z = 0 Closed spherical curve Rho=2 Theta=360*t Phi=t*360*10 Column coordinate spiral curve X = 100*t * cos (t * (5*180)) Y = 100*t * sin (t * (5*180)) Z = 0 Snake curve X = 2 * cos ((t+1) * (2*180)) Y = 2 * sin (t * (5*360)) Z = t* (t+1) 8 character curve Cylindrical coordinate Theta = t*360 R=10+ (8*sin (theta)) ^2 elliptic curve Descartes coordinate system A = 10 B = 20 Theta = t*360 X = a*cos (theta) Y = b*sin (theta) Quincunx curve Cylindrical coordinate Theta = t*360 R=10+ (3*sin (theta*2.5)) ^2 Another flower curve Theta = t*360 R=10- (3*sin (theta*3)) ^2 Z=4*sin (theta*3) ^2 A flower curve with a more spatial sense Theta = t*360 R=10- (3*sin (theta*3)) ^2 Z= (r*sin (theta*3)) ^2 A spiral of elliptic lines A = 10 B = 20 Theta = t*360*3 X = a*cos (theta) Y = b*sin (theta) Z=t*12 Even the spiral flower curve Theta = t*360*4 R=10+ (3*sin (theta*2.5)) ^2 Z = t*16 Drum line Cartesian equation R=5+3.3*sin (t*180) +t Theta=t*360*10 Z=t*10 Lock curve Cartesian equation: A=1*t*359.5 B=q2*t*360 C=q3*t*360 Rr1=w1 Rr2=w2 Rr3=w3 X=rr1*cos (a), +rr2*cos (b), +rr3*cos (c) Y=rr1*sin (a), +rr2*sin (b), +rr3*sin (c) Lock curve Cartesian equation: A=1*t*359.5 B=q2*t*360 C=q3*t*360 Rr1=w1 Rr2=w2 Rr3=w3 X=rr1*cos (a), +rr2*cos (b), +rr3*cos (c) Y=rr1*sin (a), +rr2*sin (b), +rr3*sin (c) Hairpin line Spherical coordinate Equation: Rho=200*t Theta=900*t Phi=t*90*10 Spiral curve R=t^10 Theta=t^3*360*6*3+t^3*360*3*3 Z=t^3* (t+1) Mushroom curve Rho=t^3+t* (t+1) Theta=t*360 Phi=t^2*360*20*20 8 character curve A=1 B=1 X=3*b*cos (t*360) +a*cos (3*t*360) Y=b*sin (t*360) +a*sin (3*t*360) Quincunx curve Theta=t*360 R=100+50*cos (5*theta) Z=2*cos (5*theta) Peach curve Rho=t^3+t* (t+1) Theta=t*360 Phi=t^2*360*10*10 Name: disc spring Setting up: pro/e Cylindrical sitting R = 5 Theta = t*3600 Z = (sin (3.5*theta-90)) +24 Circular two curve Cartesian equation: X=50*cos (t*360) Y=50*sin (t*360) Z=10*cos (t*360*8) Butterfly line Spherical coordinate: Rho=4*sin (t*360) +6*cos (t*360^2) Theta=t*360 Phi=log (1+t*360) *t*360 Disc spring Cylindrical coordinates Equation: r = 5 Theta = t*3600 Z = (sin (3.) 5*theta-90)) +24*t [express download,]1.jpg: Leaf line Cartesian coordinate scale Equation: a=10 X=3*a*t/ (1+ (t^3)) Y=3*a* (t^2) / (1+ (t^3)) Curve (Helical) Cylindrical coordinates (cylindrical) Equation: r=t Theta=10+t* (20*360) Z=t*3 Butterfly curve Spherical coordinate Equation: rho = 8 * t Theta = 360 * t * 4 Phi = -360 * t * 8 involute The Descartes coordinate system is adopted Equation: r=1 Ang=360*t S=2*pi*r*t X0=s*cos (ANG) Y0=s*sin (ANG) X=x0+s*sin (ANG) Y=y0-s*cos (ANG) Z=0 Helical line. Cartesian coordinates Equation: x = 4 * cos (t * (5*360)) Y = 4 * sin (t * (5*360)) Z = 10*t Logarithmic curve Descartes coordinate system Equation: z=0 X = 10*t Y = log (10*t+0.0001) Spherical helix Spherical coordinate system Equation: rho=4 Theta=t*180 Phi=t*360*20 Double arc outer cycloid Cartesian coordinates Equation: l=2.5 B=2.5 X=3*b*cos (t*360) +l*cos (3*t*360) Y=3*b*sin (t*360) +l*sin (3*t*360) Star Line Cartesian coordinates Equation: a=5 X=a* (COS (t*360)) ^3 Y=a* (sin (t*360)) ^3 Heart line Cylindrical coordinates Equation: a=10 R=a* (1+cos (theta)) Theta=t*360 Inner spiral Column coordinate system Equation: theta=t*360 R=10+10*sin (6*theta) Z=2*sin (6*theta) Sinusoidal curve Descartes coordinate system Equation: x=50*t Y=10*sin (t*360) Z=0 Fermat curve Mathematical equations: R * r = a*a*theta Cylindrical coordinates Equation 1:, theta=360*t*5 A=4 R=a*sqrt (theta*180/pi) Equation 2:, theta=360*t*5 A=4 R=-a*sqrt (theta*180/pi) Talbot curve Cartesian coordinates Equation: theta=t*360 A=1.1 B=0.666 C=sin (theta) F=1 X = (a*a+f*f*c*c) *cos (theta) /a Y = (a*a-2*f+f*f*c*c) *sin (theta) /b Rhodonea curve The Descartes coordinate system is adopted Equation: theta=t*360*4 X=25+ (10-6) *cos (theta) +10*cos ((10/6-1) *theta) Y=25+ (10-6) *sin (theta) -6*sin ((10/6-1) *theta) parabola Cartesian coordinates Equation: x = (4 * t) Y = (3 * t) + (5 * t, ^2) Z =0 Helical line Cylindrical coordinates Equation: r = 5 Theta = t*1800 Z = (COS (theta-90)) +24*t Trefoil Cylindrical coordinates Equation: a=1 Theta=t*380 B=sin (theta) R=a*cos (theta) * (4*b*b-1) Exterior cycloid DeCarr coordinate Equation: theta=t*720*5 B=8 A=5 X= (a+b) *cos (theta) -b*cos ((a/b+1) *theta) Y= (a+b) *sin (theta) -b*sin ((a/b+1) *theta) Z=0 Lissajous curve Theta=t*360 A=1 B=1 C=100 N=3 X=a*sin (n*theta+c) Y=b*sin (theta) Long and short round inner wheel Cartesian coordinates Equation: a=5 B=7 C=2.2 Theta=360*t*10 X= (a-b) *cos (theta) +c*cos ((a/b-1) *theta) Y= (a-b) *sin (theta) -c*sin ((a/b-1) *theta) Long and short round outer wheel Cartesian coordinates Equation: theta=t*360*10 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) Three cusps A=10 X = a* (2*cos (t*360) +cos (2*t*360)) Y = a* (2*sin (t*360) -sin (2*t*360)) Probability curve! Equation: Cartesian coordinates X = t*10-5 Y = exp (0-x^2) Skip line Cartesian coordinate system A = 1 X = -5 + t*10 Y = 8*a^3/ (x^2+4*a^2) Archimedes spiral Cylindrical coordinate A=100 Theta = t*400 R = a*theta Logarithmic spiral Cylindrical coordinate Theta = t*360*2.2 A = 0.005 R = exp (a*theta) Tendril line Cartesian coordinate system Helical line Spherical coordinate system Equation: rho=4 Theta=t*180 Phi=t*360*20 54. mushroom curve Rho=t^3+t* (t+1) Theta=t*360 Phi=t^2*360*20*20 Rho: represents the ratio of the anchor point to the distance between the points at the end of the two curve and the distance between the projection points on the two curve and the points at both ends. When the value is less than 1/2, an ellipse or ellipse arc is generated; when the value is equal to 1/2, a parabola is generated; when the value is greater than 1/2, a hyperbola is generated. Phi: ratio Cartesian coordinate system According to T9, change Cong 0 to 10 to R, theta, and Z For example, for a circle in the X-Y plane, the center is at the origin The radius =4, the parameter equation will be..: R=4 Theta=t*360 Z=0 Curve (Helical) Cylindrical coordinates (cylindrical) Equation: r=t Theta=10+t* (20*360) Z=t*3 Heart line Cylindrical coordinates Equation: a=10 R=a* (1+cos (theta)) Theta=t*360 A=10 Y=t*100-50 Solve X^3 = y^2* (2*a-x) For X Tan curve Cartesian coordinate system X = t*8.5 -4.25 Y = Tan (x*20) Hyperbolic cosine X = 6*t-3 Y = (exp (x) +exp (0-x)) /2 Hyperbolic sine X = 6*t-3 Y = (exp (x) -exp (0-x)) /2 35. hyperbolic tangent X = 6*t-3 Y = (exp (x) -exp (0-x)) / (exp (x) +exp (0-x))