Home› Community Support

Welcome to the Onshape forum! Ask questions and join in the discussions about everything Onshape.

First time visiting? Here are some places to start:
  1. Looking for a certain topic? Check out the categories filter or use Search (upper right).
  2. Need support? Ask a question to our Community Support category.
  3. Please submit support tickets for bugs but you can request improvements in the Product Feedback category.
  4. Be respectful, on topic and if you see a problem, Flag it.

If you would like to contact our Community Manager personally, feel free to send a private message or an email.

Primitive sphere creation from points

Dean_GardnerDean_Gardner Member Posts: 98 PRO
in Community Support
Does anyone know of a feature script that can create a 3D sphere from 3 or more points?  
Tagged:

Best Answer

  • Jacob_CorderJacob_Corder Member Posts: 137 PRO
    Answer ✓ 
    FeatureScript 2075;
import(path : "onshape/std/common.fs", version : "2075.0");


annotation { "Feature Type Name" : "Sphere 3 Point" }
export const sphereThreePoint = defineFeature(function(context is Context, id is Id, definition is map)
    precondition
    {
         annotation { "Name" : "Points", "Filter" : QueryFilterCompound.ALLOWS_VERTEX, "MaxNumberOfPicks" : 3 }
         definition.points is Query;
         
    }
    {
        var pts = [undefined,undefined,undefined];
        for(var n=0;n<3;n+=1)
        {
            pts[n] =evVertexPoint(context, {
                    "vertex" : qNthElement(definition.points, n)
            });
        }
      
       var cir =getCircleFromPoints(pts[0],pts[1],pts[2]);
       
       opSphere(context, id, {
               "radius" : cir.radius,
               "center" : cir.coordSystem.origin
       });
       
    }); 
function getCircleFromPoints(a is Vector, b is Vector, c is Vector)
{
    try silent
    { 
        var Xa = a[0] / millimeter;
        var Ya = a[1] / millimeter;
        var Za = a[2] / millimeter;
        var Xb = b[0] / millimeter;
        var Yb = b[1] / millimeter;
        var Zb = b[2] / millimeter;
        var Xc = c[0] / millimeter;
        var Yc = c[1] / millimeter;
        var Zc = c[2] / millimeter;
        // Lengths of AB, AC, AC
        var AB = (((Xa - Xb) ^ 2) + ((Ya - Yb) ^ 2) + ((Za - Zb) ^ 2)) ^ 0.5;
        var BC = (((Xb - Xc) ^ 2) + ((Yb - Yc) ^ 2) + ((Zb - Zc) ^ 2)) ^ 0.5;
        var AC = (((Xa - Xc) ^ 2) + ((Ya - Yc) ^ 2) + ((Za - Zc) ^ 2)) ^ 0.5;
        //Direction cosines of AB(ABi,ABj,ABk)
        var ABi = (Xb - Xa) / AB;
        var ABj = (Yb - Ya) / AB;
        var ABk = (Zb - Za) / AB;
        //'   Direction cosines of AC(ACi,ACj,ACk)
        //var ACi = (Xc - Xa) / AC;
        //var ACj = (Yc - Ya) / AC;
        //var ACk = (Zc - Za) / AC;
        //'   Cosine of angle BAC
        var cosBAC = (AB ^ 2 + AC ^ 2 - BC ^ 2) / (2 * AB * AC);
        var AD = cosBAC * AC;
        var CD = (AC ^ 2 - AD ^ 2) ^ 0.5;
        //'   Position of point D, which is C projected normally onto AB
        var Xd = Xa + (AD * ABi);
        var Yd = Ya + (AD * ABj);
        var Zd = Za + (AD * ABk);
        //'   Direction cosines of CD(Cdi,CDj,CDk)
        var CDi = (Xc - Xd) / CD;
        var CDj = (Yc - Yd) / CD;
        var CDk = (Zc - Zd) / CD;
        //'   Direction cosines of normal to AB and CD
        //'   — to be used for rotations of circle centre
        var Ni = (ABk * CDj) - (ABj * CDk);
        var Nj = (ABi * CDk) - (ABk * CDi);
        var Nk = (ABj * CDi) - (ABi * CDj);
        //'   # Diameter of circumscribed circle of a triangle is equal to the
        //'   the length of any side divided by sine of the opposite angle.
        //'   This is done in a coordinate system where X is colinear with AB, Y is // to CD,
        //'   and Z is the normal (N) to X and Y, and the origin is point A
        //'         R = D / 2
        var sinBAC = (1 - cosBAC ^ 2) ^ 0.5;
        var R = (BC / sinBAC) / 2;
        //'   Centre of circumscribed circle is point E
        var X2e = AB / 2;
        var Y2e = (R ^ 2 - X2e ^ 2) ^ 0.5;
        var Z2e = 0;
        //'   Transform matrix
        //'                    Rotations                 Translations
        //'             ——————————————————————————————————————————————
        //'               ABi  ,   ABj  ,  ABk                 Xa
        //'               CDi  ,   CDj  ,  CDk                 Ya
        //'                Ni  ,    Nj  ,   Nk                 Za
        //'             ——————————————————————————————————————————————
        //'   Position of circle centre in absolute axis system
        var X_centre = Xa + (X2e * ABi) + (Y2e * CDi) + (Z2e * Ni);
        var Y_centre = Ya + (X2e * ABj) + (Y2e * CDj) + (Z2e * Nj);
        var Z_centre = Za + (X2e * ABk) + (Y2e * CDk) + (Z2e * Nk);
        //'   ———————————————————————————————————————————————————————————————————

        var circleCenter = vector(X_centre * millimeter, Y_centre * millimeter, Z_centre * millimeter);
        var radius = pointDistance(circleCenter, a);
        var plane = try(planeFrom3Points(a, b, c));
        if (plane != undefined)
        {
            plane.origin = circleCenter;
            var coordsys = coordSystem(plane);
            return circle(coordsys, radius);
        }
    }
    return undefined;
}
export function pointDistance(vec0 is Vector, vec1 is Vector) returns ValueWithUnits
{ 
    var vec = [vec0[0].value - vec1[0].value, vec0[1].value - vec1[1].value, vec0[2].value - vec1[2].value]; //makeArray(size(vec0), undefined);
    return   sqrt(vec[0]*vec[0] + vec[1] *vec[1] + vec[2] *vec[2]) * meter;  
     
}
export function planeFrom3Points(pt0 is Vector, pt1 is Vector, pt2 is Vector)
{
    
    var points = [pt0, pt1, pt2];
    var normal = cross(points[2] - points[0], points[1] - points[0]);
    try silent
    {
        //check if the 3 points are on a line;
        var vec1 = points[0] - points[1];
        var vec2 = points[2] - points[1];
        if (parallelVectors(normalize(vec1), normalize(vec2)))
        {
            return undefined;
        }
    }
    try silent
    {
        var ret = plane(points[0], normalize(normal), normalize(points[1] - points[0]));
        return ret;
    }
    return undefined;
}
    This will do it.  

Answers

  • eric_pestyeric_pesty Member Posts: 1,881 PRO
    edited July 2023
    Sorry it doesn't look like I actually read what you said... Coffee hadn't kicked in yet apparently!

    Is this what you are looking for?
    https://cad.onshape.com/documents/a81f647d405a78c5b70bdbde/v/b1e90d8c768f69db42c07f9a/e/bec98f91580bad4c70005038

    Or do mean getting passed a bunch coordinates?
    Maybe using one of the "3D points" features first and then this should work (haven't tried thought)...

    Also Polyheadron:
    https://cad.onshape.com/documents/2c40f522f1b5a02f6ce9ce01/w/32e0799ad10a8f40ac24abb5/e/dd23a5b64fbc7cefbf67ffbd?renderMode=0&uiState=64b58578f6ee8b108a11e366
  • _anton_anton Member, Onshape Employees Posts: 410
    I believe you need more than 3 points to define a sphere. Also, what if they don't lie on the surface of any possible sphere or you have more points than needed? Are you looking for a bounding-sphere sort of solution?
  • Jacob_CorderJacob_Corder Member Posts: 137 PRO
    Answer ✓ 
    FeatureScript 2075;
import(path : "onshape/std/common.fs", version : "2075.0");


annotation { "Feature Type Name" : "Sphere 3 Point" }
export const sphereThreePoint = defineFeature(function(context is Context, id is Id, definition is map)
    precondition
    {
         annotation { "Name" : "Points", "Filter" : QueryFilterCompound.ALLOWS_VERTEX, "MaxNumberOfPicks" : 3 }
         definition.points is Query;
         
    }
    {
        var pts = [undefined,undefined,undefined];
        for(var n=0;n<3;n+=1)
        {
            pts[n] =evVertexPoint(context, {
                    "vertex" : qNthElement(definition.points, n)
            });
        }
      
       var cir =getCircleFromPoints(pts[0],pts[1],pts[2]);
       
       opSphere(context, id, {
               "radius" : cir.radius,
               "center" : cir.coordSystem.origin
       });
       
    }); 
function getCircleFromPoints(a is Vector, b is Vector, c is Vector)
{
    try silent
    { 
        var Xa = a[0] / millimeter;
        var Ya = a[1] / millimeter;
        var Za = a[2] / millimeter;
        var Xb = b[0] / millimeter;
        var Yb = b[1] / millimeter;
        var Zb = b[2] / millimeter;
        var Xc = c[0] / millimeter;
        var Yc = c[1] / millimeter;
        var Zc = c[2] / millimeter;
        // Lengths of AB, AC, AC
        var AB = (((Xa - Xb) ^ 2) + ((Ya - Yb) ^ 2) + ((Za - Zb) ^ 2)) ^ 0.5;
        var BC = (((Xb - Xc) ^ 2) + ((Yb - Yc) ^ 2) + ((Zb - Zc) ^ 2)) ^ 0.5;
        var AC = (((Xa - Xc) ^ 2) + ((Ya - Yc) ^ 2) + ((Za - Zc) ^ 2)) ^ 0.5;
        //Direction cosines of AB(ABi,ABj,ABk)
        var ABi = (Xb - Xa) / AB;
        var ABj = (Yb - Ya) / AB;
        var ABk = (Zb - Za) / AB;
        //'   Direction cosines of AC(ACi,ACj,ACk)
        //var ACi = (Xc - Xa) / AC;
        //var ACj = (Yc - Ya) / AC;
        //var ACk = (Zc - Za) / AC;
        //'   Cosine of angle BAC
        var cosBAC = (AB ^ 2 + AC ^ 2 - BC ^ 2) / (2 * AB * AC);
        var AD = cosBAC * AC;
        var CD = (AC ^ 2 - AD ^ 2) ^ 0.5;
        //'   Position of point D, which is C projected normally onto AB
        var Xd = Xa + (AD * ABi);
        var Yd = Ya + (AD * ABj);
        var Zd = Za + (AD * ABk);
        //'   Direction cosines of CD(Cdi,CDj,CDk)
        var CDi = (Xc - Xd) / CD;
        var CDj = (Yc - Yd) / CD;
        var CDk = (Zc - Zd) / CD;
        //'   Direction cosines of normal to AB and CD
        //'   — to be used for rotations of circle centre
        var Ni = (ABk * CDj) - (ABj * CDk);
        var Nj = (ABi * CDk) - (ABk * CDi);
        var Nk = (ABj * CDi) - (ABi * CDj);
        //'   # Diameter of circumscribed circle of a triangle is equal to the
        //'   the length of any side divided by sine of the opposite angle.
        //'   This is done in a coordinate system where X is colinear with AB, Y is // to CD,
        //'   and Z is the normal (N) to X and Y, and the origin is point A
        //'         R = D / 2
        var sinBAC = (1 - cosBAC ^ 2) ^ 0.5;
        var R = (BC / sinBAC) / 2;
        //'   Centre of circumscribed circle is point E
        var X2e = AB / 2;
        var Y2e = (R ^ 2 - X2e ^ 2) ^ 0.5;
        var Z2e = 0;
        //'   Transform matrix
        //'                    Rotations                 Translations
        //'             ——————————————————————————————————————————————
        //'               ABi  ,   ABj  ,  ABk                 Xa
        //'               CDi  ,   CDj  ,  CDk                 Ya
        //'                Ni  ,    Nj  ,   Nk                 Za
        //'             ——————————————————————————————————————————————
        //'   Position of circle centre in absolute axis system
        var X_centre = Xa + (X2e * ABi) + (Y2e * CDi) + (Z2e * Ni);
        var Y_centre = Ya + (X2e * ABj) + (Y2e * CDj) + (Z2e * Nj);
        var Z_centre = Za + (X2e * ABk) + (Y2e * CDk) + (Z2e * Nk);
        //'   ———————————————————————————————————————————————————————————————————

        var circleCenter = vector(X_centre * millimeter, Y_centre * millimeter, Z_centre * millimeter);
        var radius = pointDistance(circleCenter, a);
        var plane = try(planeFrom3Points(a, b, c));
        if (plane != undefined)
        {
            plane.origin = circleCenter;
            var coordsys = coordSystem(plane);
            return circle(coordsys, radius);
        }
    }
    return undefined;
}
export function pointDistance(vec0 is Vector, vec1 is Vector) returns ValueWithUnits
{ 
    var vec = [vec0[0].value - vec1[0].value, vec0[1].value - vec1[1].value, vec0[2].value - vec1[2].value]; //makeArray(size(vec0), undefined);
    return   sqrt(vec[0]*vec[0] + vec[1] *vec[1] + vec[2] *vec[2]) * meter;  
     
}
export function planeFrom3Points(pt0 is Vector, pt1 is Vector, pt2 is Vector)
{
    
    var points = [pt0, pt1, pt2];
    var normal = cross(points[2] - points[0], points[1] - points[0]);
    try silent
    {
        //check if the 3 points are on a line;
        var vec1 = points[0] - points[1];
        var vec2 = points[2] - points[1];
        if (parallelVectors(normalize(vec1), normalize(vec2)))
        {
            return undefined;
        }
    }
    try silent
    {
        var ret = plane(points[0], normalize(normal), normalize(points[1] - points[0]));
        return ret;
    }
    return undefined;
}
    This will do it.  
Sign In or Register to comment.

Howdy, Stranger!

It looks like you're new here. Sign in or register to get started.

Sign In

Categories

Vanilla Forums