Blender 3D: Noob to Pro/Coordinate Spaces in Blender

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This tutorial has been created with Blender v2.46

Figure 1: Objects in a three dimensional space. In the center of the coordinate system is the origin of the world coordinates.

Understanding three dimensions is one point - but how is this concept implemented in Blender?

As you have already learned, the location of an object in a three-dimensional space is defined by three descriptors (typically numbers). These three numbers make up what is called the coordinate of the location.

Blender uses the following convention: At the center of the coordinate space is its origin, the zero point. The distance from the zero point in three orthogonal directions is used to locate an object. The three directions are called the X, Y, and Z axes and are denoted by the colors red, green and blue. Viewed from the front, the X axis (red) points to the right, the Y axis (green) points to the rear, and the Z axis (blue) points upward.

[edit] Global and local coordinates

The coordinate system in the above described coordinate space is in Blender usually called the global coordinate system, though we probably should refer to it as the world coordinate system. The world coordinate system has a fixed origin and a fixed orientation, but we can view it from different angles when we rotate or pan around the world space.

The coordinates in the world coordinate system would entirely suffice, in principle, if we were working only with objects with a single vertex. But an object like the cup shown in Fig. 1 may consist of any number of vertices (in this case, the cup has 171 vertices). Therefore it is much more practical to introduce a second coordinate system: the local coordinate system. The vertices from which the cup is built are defined in the local coordinate system. The origin of the the local coordinate system is called the center of the object but is not necessarily located at the physical centre of the object. If you rotate or move the object the shape remains unaltered because the orientation of the object's local coordinate system is fixed relative to the object.

A three dimensional object is defined:

• by the vertices in its local coordinate system
• the location of the centre of the object
• the rotation of the local coordinates relative to the global coordinates

[edit] Global coordinates for objects with parents

Figure 1b: A parent serves as the source of the global coordinates for its child object. The child is the cup, the parent's orientation is shown with the colored arrows.

Animation of the above

If an object has a so called Parent, the center of its global coordinate system is no longer the position 0/0/0 of the world system, but the object center of the parent. The orientation of the global coordinates is now the orientation of the parent.

So if you move the parent, its child is moved also (without changing the child's coordinates). If you rotate the parent the child is rotated also. In this way rotations along arbitrary axes are animated.

In Fig. 1b the cup is a child object of the right coordinate cross. The child itself has no local rotation. The right coordinate cross has itself an invisible parent. It is parent and child at the same time. The right coordinate cross is rotated along its global Z axis, the tilt against the world axis is created by the invisible grandparent.

[edit] View coordinates

Figure 2: View coordinates and Projection Plane

Taking the viewer of the scene in consideration there is another coordinate space: the view coordinates. In Fig. 2 the viewer is symbolized by the camera. The Z axis of the view coordinates always points directly to the viewer in orthographic projection. The X axis points to the right, the Y axis points upwards (Fig. 3).

Figure 3: View coordinates in viewing direction

In fact you always work in view coordinates if you don't set it any other way. This is particularly handy if you have aligned your view prior to modeling something, e.g. if an object has a slanted roof and you want to create a window to fit in this roof, it would be very complicated to build this window aligned to the local coordinate system of the object, but if you first align your view to the slanted roof you can easily work in this view coordinate system.

If you work in one of the three standard views (Front/Top/Side) the alignment of the view coordinates fits the world coordinates, therefore it is quite natural to model in one of the standard views and many people find this the best way to model.

[edit] Normal coordinates

Figure 4: Normal coordinate spaces for faces. The normal is shown in blue.

Although Blender is a 3D program, only the faces are visible. The orientation of the faces is important for many reasons. For example, in our daily lives it seems quite obvious that a book lies flat on a table. This requires the surface of the table and that of the book to be parallel to each other. If we put a book on a table in a 3D program there is no mechanism that parallels the surfaces, we have to ensure that ourselves.

The orientation of a face can be described with the help of a so-called surface normal. It is always perpendicular to the surface. If several faces are selected, the resulting normal is averaged from the normals of every single face. In Fig. 4 the normal coordinates of the visible faces are drawn.

This concept can be applied to individual points on the object, even if the points themselves have no orientation. The normal of a point is the average of the adjacent faces.

Figure 5: Normal coordinates for edges

The normal definition is more useful for edges: the normal runs along the edge (Fig. 5). For example, if you want to bend an object along an edge, you simply have to bend it along its normal.