It turns out that a quadratic bezier is also relatively easy to model and demonstrates a smooth curve that STL can not represent well:
/*{
irmf: "1.0",
materials: ["PLA"],
max: [5,5,5],
min: [-5,-5,0],
units: "mm",
}*/
float interpQuadratic(vec2 p0,vec2 p1,vec2 p2,float y){
float a=p2.y+p0.y-2.*p1.y;
float b=2.*(p1.y-p0.y);
float c=p0.y-y;
if(b*b<4.*a*c){return 0.;}// bad (imaginary) quadratic
float det=sqrt(b*b-4.*a*c);
float t=(-b+det)/(2.*a);
float x=(1.-t)*(1.-t)*p0.x+2.*(1.-t)*t*p1.x+t*t*p2.x;
return x;
}
float qBezier(vec2 p0,vec2 p1,vec2 p2,in vec3 xyz){
float r=length(xyz.xy);
if(r>interpQuadratic(p0,p1,p2,xyz.z)){return 0.;}
return 1.;
}
void mainModel4(out vec4 materials,in vec3 xyz){
xyz.z+=1.;
materials[0]=qBezier(vec2(-2,2),vec2(0,0),vec2(2,2),xyz);
}-
Try loading quadratic-bezier-1.irmf now in the experimental IRMF editor!
-
Use irmf-slicer to generate an STL or voxel approximation.
We can hollow out the interior with a second quadratic bezier:
/*{
irmf: "1.0",
materials: ["PLA"],
max: [5,5,5],
min: [-5,-5,0],
units: "mm",
}*/
float interpQuadratic(vec2 p0,vec2 p1,vec2 p2,float y){
float a=p2.y+p0.y-2.*p1.y;
float b=2.*(p1.y-p0.y);
float c=p0.y-y;
if(b*b<4.*a*c){return 0.;}// bad (imaginary) quadratic
float det=sqrt(b*b-4.*a*c);
float t=(-b+det)/(2.*a);
float x=(1.-t)*(1.-t)*p0.x+2.*(1.-t)*t*p1.x+t*t*p2.x;
return x;
}
float qBezier(vec2 p0,vec2 p1,vec2 p2,in vec3 xyz){
float r=length(xyz.xy);
if(r>interpQuadratic(p0,p1,p2,xyz.z)){return 0.;}
return 1.;
}
void mainModel4(out vec4 materials,in vec3 xyz){
xyz.z+=1.;
float thickness=.5;
materials[0]=qBezier(vec2(-2,2),vec2(0,0),vec2(2,2),xyz)-
qBezier(vec2(-2,2.+thickness),vec2(0,thickness),vec2(2,2.+thickness),xyz);
}-
Try loading quadratic-bezier-2.irmf now in the experimental IRMF editor!
-
Use irmf-slicer to generate an STL or voxel approximation.
Copyright 2019 Glenn M. Lewis. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.