Texture Mapping

As we know there are couple of ways to apply texture to your model. They are basically planar, cubic, cylindrical, spherical and UV texture mapping.
Usually on every 3D application at least they have the first four methods, but recently UV texture mapping become a standard too.

Planar Mapping Method (figure 1)

Imagine if we have a picture and putting it into frame. This method works very well with flat surface, and since it is the most straight forward of all of the mapping methods, it is easily apply on organic surfaces too.

Cubic Mapping Method (figure 2)

If we arrange six of the planar map in shape of a cube then you will have a cubic mapping. Usually it is used to simulate a reflection in an environment.

Cylindrical Mapping Method (figure 3)

This method allows us to take an image map and warp it around a preferred axis (either X, Y or Z in Euler coordinate system). Imagine if we have a sticker and placing it around a Coca-Cola can. But of course on some of models like creature, this mapping may have a draw back. Most creature are rarely cylindrical, they have bumps and bends, which will stretch the texture on several spots.

Spherical Mapping Method (figure 4)

As the name implies, imagine if we have an image of earth and apply it to a ball than you will have a globe. But since sphere will have 2 poles than you will see that there will be pinching of texture at the pole position, unless that you have solid color at the top and bottom (like the ice continent on North and South Pole).

UV Mapping Method (figure 5)

This is the most difficult mapping method to understand, but it has great advantage on texturing an organic shape.
In UV Mapping method we translate the X and Y coordinate of an image into U, V coordinate of the model vertices. In some 3D application it is even possible to have U, V and W coordinate of the model vertices.
To make it simple I'm using grid as the texture and you can see how the image will be stretch and squash to follow the U and V coordinate of vertices. Usually UV Mapping comes with patches, but you could use it for polygons too. There are still problems with new kind of surface that does not have UV Coordinate, so we might see another mapping method or a gizmo/tools like Youmap that will solve the problems.