Re: Beginner and Vectors
- From: Iain <Iain@xxxxxxxxxxxxxxxxxx>
- Date: Tue, 19 Apr 2005 17:05:37 +0100
On Tue, 19 Apr 2005 08:24:57 -0700, Robert Dunlop [MS MVP] wrote:
> "Iain" <Iain@xxxxxxxxxxxxxxxxxx> wrote in message
> news:pyce8tppbi99.o8mu7q236yed$.dlg@xxxxxxxxxxxxx
>> I'm just writing my first Direct3D program, so be kind....
>>
>> I want to join some sphere's with cylinders.
>>
>> I've created my spheres and positioned them and it looks cool.
>>
>> I've created a cylinder (with Mesh.Cylinder) which is the same length as
>> the distance between the cylinders.
>>
>> what I need is a Matrix which will translate and rotate the cylinder so
>> that one end is in the first sphere and the second end is in the second
>> sphere.
>>
>> So I tried this
>>
>> private void DrawCylinder(float xStart, float yStart, float zStart, float
>> xEnd, float yEnd, float zEnd)
>
> A cylinder created with Mesh.Cylinder will have its axis along the Z-axis.
> Your application needs to rotate the cylinder so that this axis transforms
> to an axis defined by a vector between the two spheres. One way to do this
> is to determine a single axis of rotation around which to rotate the
> cylinder, and the angle of rotation required. The axis of rotation between
> the original and final orientation of the cylinder will be perpendicular to
> both the initial Z axis and the target axis, so we can use the cross product
> to determine this axis:
>
> Vector3 vZ=new Vector3(0,0,1);
> Vector3 vDif=new Vector3(xEnd-xStart,yEnd-yStart,zEnd-zStart);
> vDif.Normalize();
> Vector3 cross=Vector3.Cross(vZ,vDif);
>
> The call to Normalize() divides a vector by its own length so that the
> resulting vector has a length of one, expressing only direction rather than
> direction and distance.
>
> Next, we need to find the angle of rotation around this axis, which will be
> equal to the angle between the original Z axis and the new cylinder axis.
> We can use the dot product to determine this, which has a result equal to
> the cosine of the angle between two vectors:
>
> float dot=Vector3.Dot(vZ,vDif);
> float ang=(float) Math.Acos(dot);
>
> Finally, we can compute our transformation around the axis of rotation:
>
> Matrix mat=Matrix.Rotation(cross,ang);
>
> As you note, you'll have to add translation to this matrix so that the ends
> of the cylinder translate to the correct positions.
>
> Another option might be to use the Matrix.LookAtLH method, or implement a
> similar method based upon the algorithm shown in the docs for this function.
THanks! I shall look at this and puzzle it out!
Iain
--
Iain Downs (DirectShow MVP)
Software Product Consultant
www.idcl.co.uk
.
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