For example, when modifying your object it makes most sense to do this in local space, while calculating certain operations on the object with respect to the position of other objects makes most sense in world coordinates and so on. The reason we're transforming our vertices into all these different spaces is that some operations make more sense or are easier to use in certain coordinate systems. You probably got a slight idea what each individual space is used for. The resulting coordinates are then sent to the rasterizer to turn them into fragments. Projection to clip-space coordinates can add perspective if using perspective projection.Īnd lastly we transform the clip coordinates to screen coordinates in a process we call viewport transform that transforms the coordinates from -1.0 and 1.0 to the coordinate range defined by glViewport. Clip coordinates are processed to the -1.0 and 1.0 range and determine which vertices will end up on the screen.

After the coordinates are in view space we want to project them to clip coordinates.

Next we transform the world coordinates to view-space coordinates in such a way that each coordinate is as seen from the camera or viewer's point of view.

These coordinates are relative to some global origin of the world, together with many other objects also placed relative to this world's origin.

The next step is to transform the local coordinates to world-space coordinates which are coordinates in respect of a larger world.

Local coordinates are the coordinates of your object relative to its local origin they're the coordinates your object begins in.

The following image displays the process and shows what each transformation does: Our vertex coordinates first start in local space as local coordinates and are then further processed to world coordinates, view coordinates, clip coordinates and eventually end up as screen coordinates. To transform the coordinates from one space to the next coordinate space we'll use several transformation matrices of which the most important are the model, view and projection matrix. You're probably quite confused by now by what a space or coordinate system actually is so we'll explain them in a more high-level fashion first by showing the total picture and what each specific space represents. Those are all a different state at which our vertices will be transformed in before finally ending up as fragments. There are a total of 5 different coordinate systems that are of importance to us: The advantage of transforming them to several intermediate coordinate systems is that some operations/calculations are easier in certain coordinate systems as will soon become apparent. Transforming coordinates to NDC is usually accomplished in a step-by-step fashion where we transform an object's vertices to several coordinate systems before finally transforming them to NDC. These NDC are then given to the rasterizer to transform them to 2D coordinates/pixels on your screen. What we usually do, is specify the coordinates in a range (or space) we determine ourselves and in the vertex shader transform these coordinates to normalized device coordinates (NDC). That is, the x, y and z coordinates of each vertex should be between -1.0 and 1.0 coordinates outside this range will not be visible. OpenGL expects all the vertices, that we want to become visible, to be in normalized device coordinates after each vertex shader run. In the last chapter we learned how we can use matrices to our advantage by transforming all vertices with transformation matrices. Coordinate Systems Getting-started/Coordinate-Systems

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