A rounded object is defined by the (x,y,z) functions of the components. By making these functions themselves functions of position, we can be deform the object in interesting ways. In the following examples these deformation is a functions of x. In the illustration a simple square sectioned block is deformed by a variable amount along the x-axis. In most of these examples I have used a sine function for simplicity and familiarity but it could easily be a spline or polynomial.
 | Fig 1: shear deformation These examples can be regenerated by running the code below with the appropiate lines un-commented |
 | Fig 2: Shear deformation with surfaces at an angle to the direction of shear. |
 | Fig 3: Scale deformation. Note that the radius of the corners of the stretched faces is also stretched. |
 | Fig 4: Scale deformation with surfaces at an angle. |
 | Fig 5: Different deformation of the back and front surfaces. Shear and scale deformations can be combined so that the shape of the surfaces can be defined. |
 | Fig 6: Different deformation of the back and front surfaces. |
 | Fig 7: Twisting deformation |
 | Fig 8: Tilting deformation |
 | Fig 9: Combination of deformations 1 |
 | Fig 10: Combination of deformations 2 |
 | Fig 11: Combination of deformations 3 |
// This work is licensed under the Creative Commons Attribution 3.0 Unported License.
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// California, 94041, USA.
// Rounded objects: Illustration of deformation
// Vers: 1.00
// Date: 24 Nov 2016
// Auth: John Greenwood
#version 3.7 ;
global_settings {assumed_gamma 1.0 }
#include "Rounded_Objects.inc"
camera {location <-0,20,-60> angle 8 look_at <0,0,0> }
light_source {<-20,20,-20> colour rgb<1,1,1>}
background { color rgb<0.2, 0.4, 0.8> }
/*
//DeformSide-------------------------------------------------------------------------------------
#declare Side_y = function(x){}
#declare Side_z = function(x){0}
#declare Scale_y = function(x){1}
#declare Scale_z = function(x){1}
#declare Rotate_yz = function(x){ (0)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
//DeformScale-------------------------------------------------------------------------------------
#declare Side_y = function(x){0}
#declare Side_z = function(x){0}
#declare Scale_y = function(x){1+.3*sin(3*x)}
#declare Scale_z = function(x){1}
#declare Rotate_yz = function(x){ (0)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
//DeformRotate-------------------------------------------------------------------------------------
#declare Side_y = function(x){0}
#declare Side_z = function(x){0}
#declare Scale_y = function(x){1}
#declare Scale_z = function(x){1}
#declare Rotate_yz = function(x){pow(.3*x,3)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
//DeformTilt-------------------------------------------------------------------------------------
#declare Side_y = function(x){0}
#declare Side_z = function(x){0}
#declare Scale_y = function(x){1+.1*sin(10*x)}
#declare Scale_z = function(x){1+.1*sin(10*x)}
#declare Rotate_yz = function(x){0}
#declare Tilt_y = function(x){.2*cos(x)}
#declare Tilt_z = function(x){0}
//DeformBackFront1 p=-1 -------------------------------------------------------------------------------------
#local Front = function(x){1.5+ .6*sin(3*x)}
#local Back = function(x){1.2+.3*x}
#declare Side_y = function(x){0}
#declare Side_z = function(x){Back(x)-Front(x) }
#declare Scale_y = function(x){1}
#declare Scale_z = function(x){-.66*(Back(x)+Front(x))} //I have not worked out where the 0.66 comes from!
#declare Rotate_yz = function(x){ (0)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
*/
//DeformBackFront2 p=1 -------------------------------------------------------------------------------------
#local Front = function(x){1.5+ .6*sin(2*x)}
#local Back = function(x){1.2+ .6*sin(x)}
#declare Side_y = function(x){0}
#declare Side_z = function(x){Back(x)-Front(x) }
#declare Scale_y = function(x){1}
#declare Scale_z = function(x){-.66*(Back(x)+Front(x))}
#declare Rotate_yz = function(x){ (0)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
/*
//Deform1 -------------------------------------------------------------------------------------
#local Front = function(x){1.5+ .6*sin(3*x)}
#local Back = function(x){1.2+ .6*sin(x)}
#declare Side_y = function(x){0}
#declare Side_z = function(x){Back(x)-Front(x) }
#declare Scale_y = function(x){1}
#declare Scale_z = function(x){-.66*(Back(x)+Front(x))}
#declare Rotate_yz = function(x){ .2*x}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
//Deform2-------------------------------------------------------------------------------------
#declare Side_y = function(x){ .4*sin(1*x)}
#declare Side_z = function(x){ .4*cos(1*x)}
#declare Scale_y = function(x){ 1+.1*sin(2*x)}
#declare Scale_z = function(x){ 1+ .2*cos(3*x)}
#declare Rotate_yz = function(x){ (0)}
#declare Tilt_y = function(x){0}
#declare Tilt_z = function(x){0}
//Deform3----------------------------------------------------------------------------------------
#declare Side_y = function(x){.0}
#declare Side_z = function(x){0}
#declare Scale_y = function(x){1+.1*sin(10*x)}
#declare Scale_z = function(x){1+.1*sin(10*x)}
#declare Rotate_yz = function(x){ .2*x}
#declare Tilt_y = function(x){.2*sin(x)}
#declare Tilt_z = function(x){ .2*cos(x)}
//------------------------------------------------------------------------------------------
*/
#local Def_y = function(x,y,z){((y+Side_y(x))/Scale_y(x))*cos(Rotate_yz(x)) -((z+Side_z(x))/Scale_z(x))*sin(Rotate_yz(x))}
#local Def_z = function(x,y,z){((y+Side_y(x))/Scale_y(x))*sin(Rotate_yz(x)) +((z+Side_z(x))/Scale_z(x))*cos(Rotate_yz(x))}
#local Tiltx = function(x,y,z){(x*cos(Tilt_y(x))-y*sin(Tilt_y(x)))*cos(Tilt_z(x))-z*sin(Tilt_z(x)) }
#local Tilty = function(x,y,z){x*sin(Tilt_y(x))+y*cos(Tilt_y(x)) }
#local Tiltz = function(x,y,z){(x*sin(Tilt_z(x))+z*cos(Tilt_z(x)))*sin(Tilt_z(x))+z*cos(Tilt_z(x)) }
#declare p = 1; // change this to change the shape of the corner. 0.6 gives very close to circular
#declare r = 1; // radius when the corner is circular and surfaces are perpendicular
/*
#declare R_Object1 =
function(x,y,z){
R_Intersection(
+R_function(p,(x +(4)) /-r)
+R_function(p,(x -(4)) /+r)
+R_function(p,(z +(1.5)) /-r)
+R_function(p,(z -(1.5)) /+r)
+R_function(p,(y +(1.5)) /-r)
+R_function(p,(y -(1.5)) /+r)
)
}
#local R_Object2 =
function(x,y,z){ R_Object1(x,Def_y(x,y,z),Def_z(x,y,z)) }
isosurface {
function {
// start of rounded object ****************************************
R_Object2(Tiltx(x,y,z),Tilty(x,y,z),Tiltz(x,y,z))
// end of rounded object **************************
}
threshold 1
max_gradient 20
contained_by { box {<-4.2,-3.2, -4.2>, <4.2,3.2,4.2>} }
texture {pigment {color rgb < 1, 0.9, 0.65>}}
}