Viviani's curve with MathMod скачать в хорошем качестве

Viviani's curve with MathMod

Viviani's curve presentation with MathMod Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani(1622-1703) It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through the center of the sphere. Enjoy! MathMod download from GitHub and Sourceforge : https://sourceforge.net/projects/math... https://github.com/parisolab/mathmod/... Viviani's curve on wikipedia: https://en.wikipedia.org/wiki/Viviani... MathMod script: { "Param3D": { "Description": ["Viviani Curve by Abderrahman Taha 22/11/2020"], "Component": ["VivianiCurve","Sphere","Cylinder"], "Const": ["du=1/1000000","r=20","R=3"], "Funct": ["Cylinderx=(R/2)*cos(v)+R/2", "Cylindery=(R/2)*sin(v)", "Cylinderz=u", "Spherex=R*cos(u)*cos(v)", "Spherey=R*cos(u)*sin(v)", "Spherez=R*sin(u)", "M1v=cos(v)", "M2v=sin(v)", "Cx=R*cos(u)*cos(u)", "Cy=R*cos(u)*sin(u)", "Cz=R*sin(u)", "Rapp=u/sqrt(u*u+v*v+t*t)", "dCxu=(Cx(u+du,v,t)-Cx(u,v,t))/du", "dCyu=(Cy(u+du,v,t)-Cy(u,v,t))/du", "dCzu=(Cz(u+du,v,t)-Cz(u,v,t))/du", "axu=Rapp(dCxu(u,v,t),dCyu(u,v,t),dCzu(u,v,t))", "ayu=Rapp(dCyu(u,v,t),dCzu(u,v,t),dCxu(u,v,t))", "azu=Rapp(dCzu(u,v,t),dCxu(u,v,t),dCyu(u,v,t))", "d2Cxu=(axu(u+du,v,t)-axu(u,v,t))/du", "d2Cyu=(ayu(u+du,v,t)-ayu(u,v,t))/du", "d2Czu=(azu(u+du,v,t)-azu(u,v,t))/du", "Ax=Rapp(d2Cxu(u,v,t),d2Cyu(u,v,t),d2Czu(u,v,t))", "Ay=Rapp(d2Cyu(u,v,t),d2Czu(u,v,t),d2Cxu(u,v,t))", "Az=Rapp(d2Czu(u,v,t),d2Cxu(u,v,t),d2Cyu(u,v,t))", "nx=(ayu(u,v,t)*Az(u,v,t)-azu(u,v,t)*Ay(u,v,t))", "ny=(azu(u,v,t)*Ax(u,v,t)-axu(u,v,t)*Az(u,v,t))", "nz=(axu(u,v,t)*Ay(u,v,t)-ayu(u,v,t)*Ax(u,v,t))", "Bx=Rapp(nx(u,v,t),ny(u,v,t),nz(u,v,t))", "By=Rapp(ny(u,v,t),nz(u,v,t),nx(u,v,t))", "Bz=Rapp(nz(u,v,t),nx(u,v,t),ny(u,v,t))", "Sx=Cx(u,v,t)+(r/100)*(M1v(u,v,t)*Bx(u,v,t)+M2v(u,v,t)*Ax(u,v,t))", "Sy=Cy(u,v,t)+(r/100)*(M1v(u,v,t)*By(u,v,t)+M2v(u,v,t)*Ay(u,v,t))", "Sz=Cz(u,v,t)+(r/100)*(M1v(u,v,t)*Bz(u,v,t)+M2v(u,v,t)*Az(u,v,t))"], "Fx": ["Sx(u,v,t)","Spherex(u,v,t)","Cylinderx(u,v,t)"], "Fy": ["Sy(u,v,t)","Spherey(u,v,t)","Cylindery(u,v,t)"], "Fz": ["Sz(u,v,t)","Spherez(u,v,t)","Cylinderz(u,v,t)"], "Grid": ["200","20","60","60","60","60"], "Name": ["Viviani_Curve"], "Umax": ["2*pi","2*pi/4","3*R/2"], "Umin": ["0","-pi/2","-3*R/2"], "Vmax": ["2*pi","2*pi","2*pi"], "Vmin": ["0","0","0"] }, "Sliders": { "Max": ["20"], "Min": ["0"], "Name": ["R"], "Position": ["3"], "Step": ["1"] } }