angleBetween with a reference

EvanReese · December 2022

I'm trying to measure the angle between two 3D vectors using angleBetween(vector1, vector2, ref). I'm trying to get the visual angle of the lines when looking in the direction of ref. The help says this function returns the angle "as witnessed from the tip of a third 3-dimensional vector", which sounds like what I want, but I keep getting 90°. Am I making a mistake or just don't understand the function's intent?

Here's my test studio.

Image: https://us.v-cdn.net/5022071/uploads/editor/fh/pn5amax0s1zb.png

mahir · December 2022

Interesting problem. I took a look under the hood, and this is how angleBetween(vector1, vector2, ref) is calculating the angle. I don't get the vector math, but it is what it is.

var dotProd = dot(vector1, vector2);
var area = dot(cross(vector1, vector2), normalize(ref));
return atan2(area, dotProd);<br>

In your example, vector1 and vector2 are normal to each other, which means dotProd=0. So, regardless of what you use as the ref vector, atan2(area, dotProd) will always be -90deg. Conceptually, this doesn't seem to follow the description of the angleBetween function since it's simple enough to visualize that the vectors when projected onto a plane normal to ref do not look anywhere near perpendicular.

Seems that this is either a logic error in the function that fails in certain corner cases, or the description of the function needs to be modified to reflect the actual math being applied. That being said, it's not too difficult to do what you want manually by individually projecting each vector and then measuring the angle between them. After a little googling, it looks like a vector projection onto a plane is just that same vector with the normal portion subtracted.

var vector1p = vector1 - dot(vector1, ref)*ref;
var vector2p = vector2 - dot(vector2, ref)*ref;
var angle = angleBetween(vector1p, vector2p);

Here's a link to the modified code.

https://cad.onshape.com/documents/5e71b5547ac70bd80f596144/w/84e01b532a5be6c2f7a4c970/e/4ccf956c5319aa08f99fee65

Jacob_Corder · December 2022

Just make a plane using the direction reference and origin
then get the closest point on each using evDistance
then get one tangentLine from each edge using evEdgeTangentLine using parameter from evDistance

adjust the tangentLine to the plane using tangentLine = project(plane,tangentLine )
now call angleBetween for each tangent Line.

I never have it return 90 or neg 90, always the correct angle. if you want to be sure its the smallest angle you can simply call angleBetween 2x like this, but if you are running it a lot where a performance hit is likely, then just make sure to reverse the tangentLine if the parameter on each edge is 1 or close to 1.

var ang0 = angleBetween(tangentLine0.direction,tangentLine1.direction)
var ang1 = angleBetween(tangentLine0.direction,tangentLine1.direction*-1)
if(ang1<ang0) ang0=ang1;

this will work with all curve types.

mahir · December 2022

Interesting problem. I took a look under the hood, and this is how angleBetween(vector1, vector2, ref) is calculating the angle. I don't get the vector math, but it is what it is.

var dotProd = dot(vector1, vector2);
var area = dot(cross(vector1, vector2), normalize(ref));
return atan2(area, dotProd);<br>

In your example, vector1 and vector2 are normal to each other, which means dotProd=0. So, regardless of what you use as the ref vector, atan2(area, dotProd) will always be -90deg. Conceptually, this doesn't seem to follow the description of the angleBetween function since it's simple enough to visualize that the vectors when projected onto a plane normal to ref do not look anywhere near perpendicular.

Seems that this is either a logic error in the function that fails in certain corner cases, or the description of the function needs to be modified to reflect the actual math being applied. That being said, it's not too difficult to do what you want manually by individually projecting each vector and then measuring the angle between them. After a little googling, it looks like a vector projection onto a plane is just that same vector with the normal portion subtracted.

var vector1p = vector1 - dot(vector1, ref)*ref;
var vector2p = vector2 - dot(vector2, ref)*ref;
var angle = angleBetween(vector1p, vector2p);

Here's a link to the modified code.

https://cad.onshape.com/documents/5e71b5547ac70bd80f596144/w/84e01b532a5be6c2f7a4c970/e/4ccf956c5319aa08f99fee65

EvanReese · December 2022

got it. I also looked at that code, but I'm not great at interpreting the math. If I have to, I can make a plane(), then use evDistance() to find the points as projected on that plane and generate new angles from there, but I feel like it will be needlessly complex and not as efficient to compute as a few lines of trig. If anyone else knows what's up let me know, otherwise, I'll do what I just mentioned.

Jacob_Corder · December 2022

Just make a plane using the direction reference and origin
then get the closest point on each using evDistance
then get one tangentLine from each edge using evEdgeTangentLine using parameter from evDistance

adjust the tangentLine to the plane using tangentLine = project(plane,tangentLine )
now call angleBetween for each tangent Line.

I never have it return 90 or neg 90, always the correct angle. if you want to be sure its the smallest angle you can simply call angleBetween 2x like this, but if you are running it a lot where a performance hit is likely, then just make sure to reverse the tangentLine if the parameter on each edge is 1 or close to 1.

var ang0 = angleBetween(tangentLine0.direction,tangentLine1.direction)
var ang1 = angleBetween(tangentLine0.direction,tangentLine1.direction*-1)
if(ang1<ang0) ang0=ang1;

this will work with all curve types.

Jacob_Corder · December 2022

try this. its old code i had for measuring tangency between edges, i reversed the output to work for minimum angle. it could certainly be rewritten.

annotation { "Feature Type Name" : "Angle Between Edges" }
export const angleBetweenEdges = defineFeature(function(context is Context, id is Id, definition is map)
    precondition
    {
         annotation { "Name" : "edges", "Filter" : EntityType.EDGE, "MaxNumberOfPicks" : 2 }
         definition.edges is Query;
         annotation { "Name" : "Reference Axis", "Filter" : QueryFilterCompound.ALLOWS_AXIS, "MaxNumberOfPicks" : 1 }
         definition.axis is Query;
         
    }
    {
        var edges =evaluateQuery(context, definition.edges);
        var axisDir;
        if(isQueryEmpty(context, definition.axis)==false)
        {
            axisDir =evAxis(context, {
                    "axis" : definition.axis
            }) ;
        }
        var ang = getAngleBetweenEdges(context, edges[0], edges[1], axisDir,true);
        reportFeatureInfo(context, id, "angle: "~ ang/degree);
       
    });
 
export function getAngleBetweenEdges(context is Context, sourceEdge is Query, toEdge is Query,refPlaneLineOrDirection,showDebugEntities is boolean )
{   
    //    "arcLengthParameterization":false for speed purposes
    var sLines = evEdgeTangentLines(context, {
            "edge" : sourceEdge,
            "parameters" : [0, 1],
            "arcLengthParameterization" : false
        });
    var toLines = evEdgeTangentLines(context, {
            "edge" : toEdge,
            "parameters" : [0, 1],
            "arcLengthParameterization" : false
        });
    var dist = evDistance(context, {
            "side0" : sourceEdge,
            "side1" : toEdge,
            "arcLengthParameterization":false
        });

    var sLineIndex = dist.sides[0].parameter;
    var toLineIndex = dist.sides[1].parameter;
    //now we correct the deviation found in the return parameterization to determine direction for min angle between
    if (sLineIndex - .1 < 0)
    {
        sLineIndex = 0;
    }
    else if (sLineIndex + .1 > 1)
    {
        sLineIndex = 1;
    }
    if (toLineIndex - .1 < 0)
    {
        toLineIndex = 0;
    }
    else if (toLineIndex + .1 > 1)
    {
        toLineIndex = 1;
    }
    if(refPlaneLineOrDirection is Vector) refPlaneLineOrDirection = plane(zeroVector(3)*meter  , refPlaneLineOrDirection);
    if(refPlaneLineOrDirection is Line) refPlaneLineOrDirection = plane(refPlaneLineOrDirection.origin,refPlaneLineOrDirection.direction);
    if(refPlaneLineOrDirection is Plane)
    {        
        toLines[toLineIndex] = project(refPlaneLineOrDirection, toLines[toLineIndex]);
        sLines[sLineIndex] = project(refPlaneLineOrDirection, sLines[sLineIndex]);        
    }
    
    if(toLineIndex ==1)
    {
        toLines[toLineIndex].direction *=-1;
    }
    if(sLineIndex ==1)
    {
        sLines[sLineIndex].direction *=-1;
    }
    if(showDebugEntities==true)
    {
         var int =intersection(toLines[toLineIndex], sLines[sLineIndex]);
         if(refPlaneLineOrDirection is Plane && int.dim ==0) refPlaneLineOrDirection.origin = int.intersection;
        if(int.dim ==0 && dist.distance > .5*millimeter)
        {
            try silent(addDebugArrow(context, toLines[toLineIndex].origin, int.intersection, .25 * millimeter, DebugColor.RED));
            try silent(addDebugArrow(context, sLines[sLineIndex].origin, int.intersection, .25 * millimeter, DebugColor.GREEN));
        }
        else
        {
            try(addDebugArrow(context, toLines[toLineIndex].origin, toLines[toLineIndex].origin + toLines[toLineIndex].direction*(10*millimeter), .25 * millimeter, DebugColor.RED));
            try(addDebugArrow(context, sLines[sLineIndex].origin, sLines[sLineIndex].origin + sLines[sLineIndex].direction*(10*millimeter), .25 * millimeter, DebugColor.GREEN));
        }
    }
    return angleBetween(toLines[toLineIndex].direction, sLines[sLineIndex].direction  );
    
}

EvanReese · December 2022

Jacob_Corder said:

Just make a plane using the direction reference and origin
then get the closest point on each using evDistance
then get one tangentLine from each edge using evEdgeTangentLine using parameter from evDistance

adjust the tangentLine to the plane using tangentLine = project(plane,tangentLine )
now call angleBetween for each tangent Line.

I never have it return 90 or neg 90, always the correct angle. if you want to be sure its the smallest angle you can simply call angleBetween 2x like this, but if you are running it a lot where a performance hit is likely, then just make sure to reverse the tangentLine if the parameter on each edge is 1 or close to 1.

var ang0 = angleBetween(tangentLine0.direction,tangentLine1.direction)
var ang1 = angleBetween(tangentLine0.direction,tangentLine1.direction*-1)
if(ang1<ang0) ang0=ang1;

this will work with all curve types.

@Jacob_Corder
That's pretty similar to what I was going to do, but I like your way using project() instead of evDistance(), which is more roundabout. I don't think I've used that function before. Thanks for the tip. I got it working.

EvanReese · December 2022

I'll dig into your longer code when I have time, but I have a function working for now. Thanks so much!

mahir · December 2022

Evan_Reese said:

got it. I also looked at that code, but I'm not great at interpreting the math. If I have to, I can make a plane(), then use evDistance() to find the points as projected on that plane and generate new angles from there, but I feel like it will be needlessly complex and not as efficient to compute as a few lines of trig. If anyone else knows what's up let me know, otherwise, I'll do what I just mentioned.

If you want to minimize code and processing time, I think my solution above does the trick with minimal trig and only one call to angleBetween. I think it uses 2 more lines of code than your original FS just to generate vector1p and vector2p using speedy vector math.

Edit: Nevermind. Looks like using project() is even more straightforward along with a wrapper function. Cheers.

EvanReese · December 2022

Hey @mahir
I must have read your reply too quickly and missed that part. So sorry! You absolutely answered my question and I've marked it as such.

Jacob_Corder · December 2022

If you guys want fast, get rid of vectors, planes, lines. use numerics only, that is what I do. Use onshapes @functions @evEdgeTangentLines is 3x faster than evEdgeTangentLines. @evDistance is much faster than evDistance. Planes take time to create, so do lines. angleBetween can be optimized by getting rid of the vectors and its for loops within the code. norm is one of the most inefficient pieces of code ive seen since it deals with vectors. my pointDistance code is over 4x faster than onshapes norm function.

basically, if you are pinching milliseconds, use only numeric values and arrays, or skip arrays and use x, y , z

angleBetween with a reference

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