### Viewing the world

Default you look along the negative z-axis toward the middle of the room. Often in 3D games you want to change how you look at the world. For example, in a first person shooter you probably want to have the camera look from a position a bit above the xy-plane along the xy-plane. In graphics terms you are setting the correct projection. To change the way you look the following two functions exist.

d3d_set_projection(xfrom,yfrom,zfrom,xto,yto,zto,xup,yup,zup) Defines how to look in the world. You specify the point to look from, the point to look to and the up vector.

This function requires some explanation. To set the projection you first need the position you look from. This is indicated by the parameters (xfrom,yfrom,zfrom). Next you must specify the direction you look in. This is done by giving a second point to look towards. This is the point (xto,yto,zto). Finally, you can still rotate the camera around the line from the viewpoint to the looking point. To specify this we must give an up vector, that is, the direction that is upwards in the camera. This is given by the last three parameters (xup,yup,zup). Let me given an example. To look along the xy-plane as in a first person shooter you can use

```{
d3d_set_projection(100,100,10,200,100,10,0,0,1);
}
```
So you look from point (100,100) and 10 above the plane in the direction of (200,100). The up vector points is the z-direction as required. To make this slightly more complicated, assume you have an instance in your room that specifies the position of the camera. It will have a current (x,y) position and a direction (and maybe even a speed). You can now specify this as your camera by using the following code:

```{
with (obj_camera)
d3d_set_projection(x,y,10,
x+cos(direction*pi/180),y-sin(direction*pi/180),10,
0,0,1);
}
```

This might look a bit complicated. We look from the camera position (x,y), 10 above the ground. To determine a point in the correct direction we need to do a little arithmetic. This point is indicated by the next three parameters. Finally we use the up vector as above.

One important remark! When GameMaker starts drawing a room it will set the view point back to the default position. So the first thing you must do when drawing the scene is set is to the projection you want. This must be done in a drawing event!

There is also an extended version of the function above:

d3d_set_projection_ext(xfrom,yfrom,zfrom,xto,yto,zto,xup,yup,zup,angle,aspect,znear,zfar) An extended version of this function in which you also specify the angle defining the field of view, the aspect ratio between horizontal and vertical size of the view, and the near and far clipping planes.

The additional parameters work as follows. If you specified the camera position, point to look at, and up vector, you can still change how wide the lens of the camera is. This is called the field of view. A reasonable value is somewhere between 40 and 45 degrees. But you can change this if you like. Next you can specify the aspect ratio between the horizontal and vertical projection. Normally you want to use the same as the aspect ration of the room or view, e.g. 640/480. Finally you can indicate the clipping planes. Objects that are closer than znear to the camera are not drawn. Similar for objects further than zfar. It can be important to set these parameters to reasonable values because they also influence the precision of the z-comparisons. If you make the range too large the precision gets worse. Default we use 1 and 32000. znear must be larger than 0!

Sometimes you temporarily need a normal orthographic projection as is used when there is no 3D. Or you want to return to the default perspective projection. For this you can use the following functions:

d3d_set_projection_ortho(x,y,w,h,angle) Sets a normal orthographic projection of the indicated area in the room, rotated over the indicated angle.
d3d_set_projection_perspective(x,y,w,h,angle) Sets a normal perspective projection of the indicated area in the room, rotated over the indicated angle.

A standard use for this is to draw an overlay to e.g. show the score or other aspects. To do so we set an orthographic projection. We also must temporarily switch off hidden surface removal cause we want the information to be drawn regardless of the current depth value. The following example shows how to create an overlay with the score.

```{
draw_set_color(c_black);
d3d_set_projection_ortho(0,0,room_width,room_height,0);
d3d_set_hidden(false);
draw_text(10,10,'Score: ' + string(score));
d3d_set_hidden(true);
}
```

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