Flip 3D object around point/line

Question

I'm making a 3D monster maker. I recently added a feature to flip parts along the x and y axes, this works perfectly fine on its own, however, I also have a feature that allows users to combine parts (sets flags, doesn't combine mesh), this means that simply flipping the individual objects won't flip the "shape" of the combined object. I have had two ideas of how to do this which didn't work and I'll list them below. I have access to the origin of the objects and the centre of mass of all instances that are combined - the 0, 0, 0 point on a theoretical number plane

In these examples we're flipping across the y axis, the axis plane is X = width, Y = height, Z = depth

Attempt #1 - Simply flipping the individual object's X scale, getting the X distance from the centreMass and taking that from the centreMass for position, this works when the direction of the object is (0, 0, 1) and the right (1, 0, 0) or (-1, 0, 0), in any other direction X isn't the exact "left/right" of the object. Here's a video to clarify: https://youtu.be/QXdEF4ScP10

code:

modelInstance[i].scale.x *= -1;
modelInstance[i].basePosition.set(centre.x - modelInstance[i].distFromCentre.x, modelInstance[I].basePosition.y, modelInstance[I].basePosition.z);
modelInstance[i].transform.set(modelInstance[i].basePosition, modelInstance[i].baseRotation, modelInstance[i].scale);

Attempt #2 - Rotate the objects Y180° around the centreMass and then flip their z value. As far as I understand, this is a solution, but I don't think I can do this. The way to rotate an object around a point AFAIK involves transforming the matrix to the point, rotating it, and then translating it back which I can't use. Due to the ability to rotate, join, flip, and scale objects I keep the rotation, position, and scale completely separate because issues with scaling/rotating and movement occur. I have a Vector3 for the position, a matrix for the rotation, and a Vector3 for the scale, whenever I change any of these I use object.transform.set(position, matrix.getRotation(), scale); So when I attempt to do this method (translating rotation matrix to point etc) the objects individually flip but remain in the same place, translating the objects transform matrix has weird results and doesn't work. Video of both variations: https://youtu.be/5xzTAHA1vCU

code:

modelInstance[i].scale.z *= -1;
modelInstance[i].baseRotationMatrix.translate(modelInstance[i].distFromCentre).rotate(Vector3.Y, 180).translate( modelInstance[i].distFromCentre.scl(-1));
modelInstance[i].transform.set(modelInstance[i].basePosition, modelInstance[i].baseRotation, modelInstance[i].scale);

Answer 1

Ok, since no one else has helped I'll give you some code that you can either use directly or use to help you alter your code so that it is done in a similar way.

First of all, I tend to just deal with matrices and pass them to shaders as projection matrices, ie. I don't really know what modelInstance[i] is, is it an actor (I never use them), or some other libgdx class? Whatever it is, if you do use this code to generate your matrices, you should be able to overwrite your modelInstance[i] matrix at the end of it. If not, maybe it'll give you pointers on how to alter your code.

First, rotate or flip your object with out any translation. Don't translate or scale first, because when you rotate you'll also rotate the translation you've performed. I use this function to generate a rotation matrix, it rotates around the y axis first, which I think is way better then other rotation orders. Alternatively you could create an identity matrix and use the libgdx rotation functions on it to create a similar matrix.

  public static void setYxzRotationMatrix(double xRotation, double yRotation, double zRotation, Matrix4 matrix)
  {
    // yxz - y rotation performed first
    float c1=(float)Math.cos(yRotation);
    float c2=(float)Math.cos(xRotation);
    float c3=(float)Math.cos(zRotation);
    float s1=(float)Math.sin(yRotation);
    float s2=(float)Math.sin(xRotation);
    float s3=(float)Math.sin(zRotation);

    matrix.val[0]=  -c1*c3 - s1*s2*s3;  matrix.val[1]=c2*s3;    matrix.val[2]=c1*s2*s3-c3*s1;               matrix.val[3]=0;
    matrix.val[4]=  -c3*s1*s2 + c1*s3;  matrix.val[5]=c2*c3;    matrix.val[6]=c1*c3*s2+s1*s3;    matrix.val[7]=0;
    matrix.val[8]=  -c2*s1;             matrix.val[9]=-s2;      matrix.val[10]=c1*c2;            matrix.val[11]=0;
    matrix.val[12]=0;                   matrix.val[13]=0;       matrix.val[14]=0;                   matrix.val[15]=1.0f;
  }

I use the above function to rotate my object to the correct orientation, I then translate it to the correct location, then multiply it by the cameras matrix and scale as the final operation. This will definitely work if you can do it that way, but I just pass my final matrix to the shader. I'm not sure how you use your matrices. If you want to flip the model using the scale, you should try it immediately after the rotation matrix has been created. I'd recommend getting it working without flipping with scale first, so you can test both matrix.scl() and matrix.scale() as the final step. Off hand, I'm not sure which scale function you'll need.

Matrix4 matrix1;
setYxzRotationMatrix(xRotationInRadians, yRotationInRadians, zRotationInRadians,matrix1);
//matrix1 will rotate your model to the correct orientation, around the origin.

//here is where you may wish to use matrix1.scl(-1,1,1) or matrix1.scale(-1,1,1).

//get anchor position here if required - see notes later

//now translate to the correct location, I alter the matrix directly so I know exactly
what is going on. I think matrix1.trn(x, y, z) would do the same.
matrix1.val[12]=x;
matrix1.val[13]=y;
matrix1.val[14]=z;

//Combine with your camera, this may be part of your stage or scene, but I don't use
//these, so can't help.
Matrix4 matrix2;
//set matrix2 to an identity matrix, multiply it by the cameras projection matrix, then
//finally with your rotation/flip/transform matrix1 you've created. 
matrix2.idt().mul(yourCamera.combined).mul(matrix1); 

matrix2.scale(-1,1,1); //flipping like this will work, but may screw up any anchor
                       //position if you calculated one earlier.

//matrix2 is the final projection matrix for your model. ie. you just pass that matrix
to a shader and it should be used to multiply with each vertex position vector to create
the fragment positions.

Hopefully you'll be able to adapt the above to your needs. I suggest trying one operation at a time and making sure your next operation doesn't screw up what you've already done.

The above code assumes you know where you want to translate the model to, that is you know where the center is going to be. If you have an anchor point, lets say -3 units in the x direction, you need to find out where that anchor point has been moved to after the rotation and maybe flip. You can do that by multiplying a vector with matrix1, I'd suggest before any translation to the correct location.

Vector3 anchor=new vector3(-3,0,0);
anchor.mul(matrix1); //after this operation anchor is now set to the correct location
                     //for the new rotation and flipping of the model. This offset should
                     //be applied to your translation if your anchor point is not at 0,0,0
                     //of the model.

This can all be a bit of a pain, particularly if you don't like matrices. It doesn't help that everything is done in a different way to what you've tried so far, but this is the method I use to display all the 3D models in my game and will work if you can adapt it to your code. Hopefully it'll help someone anyway.