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22/12/2017

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#indian genius mathematics read Story

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http://www.allnationalknowledge.in/2018/06/you-must-experience-who-is-indian.html

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Animation and the morph effect(part 1)

One of the greatest feature in MathMod is it's ability to accomplish simple animation and morph effects by using the t-time parameter. Mastering this feature to let it do exactly what you need isn't an easy task though, especially when dealing with complex math models or a set of math objects...

Sometimes, the way your math object was modelled can give a clue on how to create an animation according to your needs. The attached animation is a good example of this concept: The complex torus's rotational movement is in fact the result of applying a "simple" straight (rectilinear) movement to each Schwarz building block at the step 3 , when they were still aligned on a planner form (see the second attached image that depicts the steps it took to model this math object). So, a rectilinear movement end up as a rotational movement in the final result!!

The attached script is a modified version from MathMod scripts collection and the only difference come from this line, with the introduction of the term "-3*t" :

"isoTransform=if(x*x<10.24,SchwarzP(x,y,z-3*t,t),1)+0.1*M*exp(x*x-9)",

The "z-3*t" means that every SchwarzP building bloc will move with a speed of "3*t" along the z-axis

Hope this introduction to the morph effect isn't too much scary and will give you some clue on how to accomplish your own animations :-)

MathMod script:

{

"Iso3D": {

"Description": ["Schwarz P Tori-1.0 by Abderrahman Taha 25/02/2016"

], "Component": ["Schwarz P Tori"

],

"Const": ["M=1","N1=15","N2=15","R1=8","R2=15","H=4"

],

"Funct": ["Iso=cos(x)+cos(y)+cos(z)","R=0.1*H*x/sqrt(x*x+y*y+z*z)","Iso4= (Iso(x+R(sin(x),sin(y),sin(z),t),y+R(sin(y),sin(x),sin(z),t), z+R(sin(z),sin(y),sin(x),t),t))","Iso5= (Iso(x-R(sin(x),sin(y),sin(z),t),y-R(sin(y),sin(x),sin(z),t), z-R(sin(z),sin(y),sin(x),t),t))","SchwarzP= (Iso4(x,y,z,t)*Iso5(x,y,z,t))","isoTransform=if(x*x<11.24,SchwarzP(x,y,z-3*t,t),1)+0.1*M*exp(x*x-11)","isoTransform2=isoTransform((sqrt(x*x+z*z)-R1),y,N1*atan2(z,x),t)"

],

"Fxyz": ["-isoTransform2((sqrt(x*x+y*y)-R2),N2*atan2(y,x),z,t)"

],

"Name": ["SchwarzP_Tori"

],

"Xmax": ["27"

],

"Xmin": ["-27"

],

"Ymax": ["27"

],

"Ymin": ["-27"

],

"Zmax": ["12"

],

"Zmin": ["-12"

]

},

"Sliders": {

"Max": ["20","20","20","15","25","30","20","20","20","15","25","30","20","20","20","15","25","30"

],

"Min": ["0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"

],

"Name": ["H","N1","N2","R1","R2","M"

],

"Position": ["4","15","15","8","15","1","4","3","13","8","16","0","5","7","9","8","16","0"

],

"Step": ["1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1"

]

}

}

One of the greatest feature in MathMod is it's ability to accomplish simple animation and morph effects by using the t-time parameter. Mastering this feature to let it do exactly what you need isn't an easy task though, especially when dealing with complex math models or a set of math objects...

Sometimes, the way your math object was modelled can give a clue on how to create an animation according to your needs. The attached animation is a good example of this concept: The complex torus's rotational movement is in fact the result of applying a "simple" straight (rectilinear) movement to each Schwarz building block at the step 3 , when they were still aligned on a planner form (see the second attached image that depicts the steps it took to model this math object). So, a rectilinear movement end up as a rotational movement in the final result!!

The attached script is a modified version from MathMod scripts collection and the only difference come from this line, with the introduction of the term "-3*t" :

"isoTransform=if(x*x<10.24,SchwarzP(x,y,z-3*t,t),1)+0.1*M*exp(x*x-9)",

The "z-3*t" means that every SchwarzP building bloc will move with a speed of "3*t" along the z-axis

Hope this introduction to the morph effect isn't too much scary and will give you some clue on how to accomplish your own animations :-)

MathMod script:

{

"Iso3D": {

"Description": ["Schwarz P Tori-1.0 by Abderrahman Taha 25/02/2016"

], "Component": ["Schwarz P Tori"

],

"Const": ["M=1","N1=15","N2=15","R1=8","R2=15","H=4"

],

"Funct": ["Iso=cos(x)+cos(y)+cos(z)","R=0.1*H*x/sqrt(x*x+y*y+z*z)","Iso4= (Iso(x+R(sin(x),sin(y),sin(z),t),y+R(sin(y),sin(x),sin(z),t), z+R(sin(z),sin(y),sin(x),t),t))","Iso5= (Iso(x-R(sin(x),sin(y),sin(z),t),y-R(sin(y),sin(x),sin(z),t), z-R(sin(z),sin(y),sin(x),t),t))","SchwarzP= (Iso4(x,y,z,t)*Iso5(x,y,z,t))","isoTransform=if(x*x<11.24,SchwarzP(x,y,z-3*t,t),1)+0.1*M*exp(x*x-11)","isoTransform2=isoTransform((sqrt(x*x+z*z)-R1),y,N1*atan2(z,x),t)"

],

"Fxyz": ["-isoTransform2((sqrt(x*x+y*y)-R2),N2*atan2(y,x),z,t)"

],

"Name": ["SchwarzP_Tori"

],

"Xmax": ["27"

],

"Xmin": ["-27"

],

"Ymax": ["27"

],

"Ymin": ["-27"

],

"Zmax": ["12"

],

"Zmin": ["-12"

]

},

"Sliders": {

"Max": ["20","20","20","15","25","30","20","20","20","15","25","30","20","20","20","15","25","30"

],

"Min": ["0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"

],

"Name": ["H","N1","N2","R1","R2","M"

],

"Position": ["4","15","15","8","15","1","4","3","13","8","16","0","5","7","9","8","16","0"

],

"Step": ["1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1"

]

}

}

21/05/2018

2 Photos - View album

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