CODEWITHSUNDEEP
c#wpfmatrix3d
user316117
user316117

Reputation: 8281

Use of offsets for translation in Matrix3D

I have an application where I want to scale, rotate, and translate some 3D points.

I'm used to seeing 3x3 rotation matrices, and storing translation in a separate array of values. But the .Net Matrix3D structure ( https://msdn.microsoft.com/en-us/library/System.Windows.Media.Media3D.Matrix3D%28v=vs.110%29.aspx) is 4x4 and has a row of "offsets" - OffsetX, OffsetY, OffsetZ, which are apparently used for translation. But how, exactly, are they intended to be applied?

Say I have a Vector3D with X, Y, Z values, say 72, 24, 4. And say my Matrix3D has

.707   0   -.707   0
0      1     0     0
.707   0   .707    0
100   100    0     1

i.e., so the OffsetX and OffsetY values are 100.

Is there any method or operator for Matrix3D that will apply this as a translation to my points? Transform() doesn't seem to. If my code has . . . 

Vector3D v = new Vector3D(72, 24, 0);
Vector3D vectorResult = new Vector3D();
vectorResult = MyMatrix.Transform(v);

vectorResult has 8.484, 24, -8.484, and it has the same values if the offsets are 0.

Obviously I can manually apply the translation individually for each axis, but I thought since it's part of the structure there might be some method or operator where you give it a point and it applies the entire matrix including translation. Is there?

Upvotes: 1

Views: 1332

Answers (1)

Nico Schertler
Nico Schertler

Reputation: 32617

A 4x4 matrix represents a transform in 3D space using homogeneous coordinates. In this representation, a w component is added to the vector. This component differs based on what a vector should represent. Transforming a vector with the matrix is simple multiplication:

transformed = vector * matrix

(where both vectors are row-vectors).

The w component is only considered by the matrix' last row - the part where the translation is stored. So if you want to transform points, this component needs to be 1. If you want to transform directions, this component needs to be 0 (because direction vectors do not change if you translate them).

This difference is expressed with two different structures in WPF. The Vector3D represents a direction (with w component 0) and the Point3D represents a point (with w component 1). So if you make v a Point3D, everything should work as you expect.

Upvotes: 3

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