6.3 - Translating¶
Translating a model changes the model’s location. Translation does not affect the
model’s size or orientation. Mathematically, translating is a simple
addition. Translating a vertex, (x, y, z), into a new location,
(x_new, y_new, z_new), is accomplished by adding a value to each component.
Let’s call these translation values tx, ty, and tz. In equation format,
translation is performed like this:
x_new = x + tx;
y_new = y + ty;
z_new = z + tz;
Notice that translating by 0 leaves a component value unchanged. Vertices are typically manipulated as a unit, so if you want to translate along one axis and leave the other axes unchanged, use a translation value of 0 for the unchanged axes.
Special Cases and Effects¶
There are no “special cases” for translation. Experiment with the following example.
An example of translating a model.
X translation 0.00 : -2.0 2.0
Y translation 0.00 : -2.0 2.0
Z translation 0.00 : -2.0 2.0
To negate (or undo) a translation operation, simply translate using a
negative (-tx, -ty, -tz) translation. For example, if you translated a
model by (2, -3, 1), then translating by (-2, 3, -1) puts it back
in its original location.
Glossary¶
- translate
- Change the location of a model.
Self Assessment¶
-
Q-126: Translating a model requires a(n) _____________ operation on each vertex in the model.
- addition
- Correct. Addition is used for translation.
- multiplication
- Incorrect. Multiplication performs scaling.
- division
- Incorrect. Division performs scaling.
- subtraction
- Subtraction does perform translation, but we normally think of translation as pure addition. To move "backwards" you add a negative value.
-
Q-127: Translating a model 3 units in the direction of the x axis would use which translation values.
- 3, 0, 0
- Correct. The x-axis component gets increased by 3 units and the y and z components do not change.
- 3
- Incorrect. Translation acts on a vertex, which has 3 components. You need 3 translation values, even if 2 of the components are not changing.
- 0, 0, 3
- Incorrect. This would move 3 units in the direction of the z axis.
- 1.5
- Incorrect. Translation uses addition. (And you need 3 translation values, not just 1.)
-
Q-128: Translating a model in the direction of a vector <dx, dy, dz> would use what translation values?
- dx, dy, dz
- Correct. You add the vector to every vertex in the model.
- dy, dz, dx
- Incorrect. The values you add must be consistent with the vertex component values (x, y, z).
- 1, 2, 3
- Incorrect. These values would move 1 unit in the x direction, 2 units in the y direction, and 3 units in the z direction, but this has nothing to do with the vector
- tx, ty, tz
- Incorrect. In general we have 3 translation values, and we generically call them tx, ty, and tz, but this has nothing to do with the vector