# 3D Stage

The 3D Stage, named after the stages that plays are performed on, is a concept that allows displayables to be positioned in 3 dimensions. Ren'Py will then render the displayables with the proper perspective, and will also make the z dimension avalable, to make things like lighting and depth rendering possible.

## Coordinates

Probably the most important thing to understand about the 3D Stage is the coordinate system that Ren'Py uses for the 3D state. Here's the coordinate system that's used to place displayables in 2D:

In 2D, the rectangle is the size of the screen, and the width and height of the visible area is set using `gui.init()` (usually when first making a new game).

The 3D stage extends this coordinate system with a new axis, one facing towards the viewer, so that values greater than 0 bring an image closer (and make it bigger), and those less than 0 move the image away from the viewer (and make it smaller).

Finally, when a rotation in 3d happens, it's in the directions given here:

- When rotating around Z, X moves toward Y.
- When rotating around X, Y moves toward Z.
- When rotating around Y, Z moves toward X.

These coordinate systems are based on those used in Ren'Py, making it easy to move from 2D to the 3D stage. When importing 3D models, coordinate transforms may be applied to ensure the model coordinates are sensible.

## Camera

The initial placement of the camera is controlled by the parameters to `gui.init()`. First, Ren'Py uses width and fov to compute the default z distance. For the default fov of 75:

- When width = 1280, z is about 834
- When width = 1920, z is about 1251
- When width = 3840, z is about 2502

Where the actual value of z is less than 1 higher than the values given here. The default z placement can be overridden with the `perspective` style property, or the `config.perspective` variable.

Ren'Py automatically applies an offset of (width / 2, height / 2, z) to the camera, and it looks down the -Z axis.

The z distance is also the distance from the camera to the plane where pixels on-screen have the same size as they do in the original images (ignoring window scaling). Increasing the camera's z position will make everything smaller, while decreasing it will make everything bigger.

Finally, `perspective` and `config.perspective` describe the near and far planes, defaulting to 100 and 100000, respectively. This means than when an image is closer than 100 z-units from the camera, it disappears, and it also disappears if it's more than 100,000 z-units away.

## Using the 3D Stage

The first thing to do to use the 3D stage is to enable it for a layer, using the `camera` statement. This is usually done with:

    camera:
        perspective True

though it's possible that you'll want to include a default camera position, as described below.

Showing images (backgrounds and sprites) works the same way as it does in when using 2D coordinates.

    scene bg washington

    show lucy mad at right

    show eileen happy

However, it's possible to use transforms to move these displayables in three dimensional space:

    scene bg washington:
        xalign 0.5 yalign 1.0 zpos -1000

    show lucy mad:
        xalign 1.0 yalign 1.0 zpos 100

    show eileen happy:
        xalign 0.5 yalign 1.0 zpos 200

As an ATL transform is given, the default transform is not used, and it's necessary to specify `xalign` and `yalign` to position the displayable in the x and y axes. Of course, transforms can also be used.

    transform zbg:
        zpos -100

    transform z100:
        zpos 100

    transform z200:
        zpos 200

    scene bg washington at center, zbg

    show lucy mad at right, z100

    show eileen happy at center, z200

If you try this, you'll see an empty space around the background. That's because by moving it back, it becomes smaller, and doesn't fill the screen. Ren'Py has an easy way of fixing this problem - `zzoom`. Setting the tpref:zzoom property to True will scale an image by the amount it was shrunk due to having a negative zpos. It's useful for backgrounds.

    transform zbg:
        zpos -100 zzoom False

It's also possible to use ATL to vary zpos, just like you would xpos and ypos.

    show eileen happy at center:
        zpos 0
        linear 4.0 zpos 200

Note that zpos can interact strangely with positions like `left` and `right`, and with `xalign` and `yalign`. That's because Ren'Py will position the images in a three dimensional rectangular volume (like a cube, but not all the sides are the same length), and then apply perspective to the image, which can cause parts of the image to move offscreen.

It's possible to move the camera, as well, using `camera`. For example,

    camera:
        perspective True
        xpos 0
        linear 3.0 xpos 500

When doing this, it probably makes sense to use background images that are larger than the window.

If you apply a zpos to a sprite, and it doesn't take effect, the reason is probably because you omitted the `perspective` clause of the `camera` transform.

The camera can be rotated, with:

    camera:
        perspective True
        rotate 45

As the camera is what is rotating, the rotation is in the opposite direction as one that rotates a displayable.

## Depth

By default, Ren'Py will display the images in its usual order, with the last image to be shown above the others. This might lead to odd results, like an image that is closer (using perspective) beign shown behind one that's farther away.

If your game shows images out of order like this, you can tell the GPU to sort by depth, using `gl_depth`:

    camera:
        perspective True
        gl_depth True

Slight rounding errors can cause images that are nominally at the same depth to appear above or below each other. Flattening these images and displaying them together may be the solution to this.

## Matrix Transforms

Ren'Py uses the `matrixtransform` transform property to apply a matrix to displayables, which allows an image to be scaled, offset, and rotated in three-dimensional space. This property takes either a `Matrix()` or a TransformMatrix (defined below), and applies it to the vertices at the corners of the images being displayed.

Ren'Py uses the `matrixanchor` transform property to make applying a matrix easier. This defaults to (0.5, 0.5), and is translated to a pixel offset inside the image being transformed using the usual Ren'Py anchor rules. (If it's an integer or abolute, it's considered a number of pixels, otherwise it's a fraction of the size of the image.)

Ren'Py applies the image by first shifting the image so the anchor is at (0, 0, 0). It then applies the transform, and then shifts it back by the same amount. Using the defaults, this means that the matrix will be applied to the center of the image.

For example:

    show eileen happy at center:
        matrixtransform RotateMatrix(45, 0, 0)

Will rotate the image around the line going horizontally through it's center. The top of the image will move back, and then bottom of the image will move forwards.

Matrixes can be chained together with multiplication. It's easiest to think about them being applied right to left. In this example:

    show eileen happy at center:
        matrixtransform RotateMatrix(45, 0, 0) * OffsetMatrix(0, -300, 0)

The image will be shifted up by 300 pixels, and then will be rotated around the X axis.

### Structural Similarity

In ATL, interpolating a the `matrixtransform` property requires the use of TransformMatrixes that have structural similarity. That means the same types of TransformMatrix, multiplied together in the same order.

As an example, the following will rotate and offset, then move back:

    show eileen happy at center:
        matrixtransform RotateMatrix(0, 0, 0) * OffsetMatrix(0, 0, 0)
        linear 2.0 matrixtransform RotateMatrix(45, 0, 0) * OffsetMatrix(0, -300, 0)
        linear 2.0 matrixtransform RotateMatrix(0, 0, 0) * OffsetMatrix(0, 0, 0)

While the first setting of matrixtransform may seem unnecessary, it is required to provide a base for the first linear interpolation. If it wasn't present, that interpolation would be skipped.

## TransformMatrix

While Matrix objects are suitable for static transformations, they're not useful for animating changing transformations. It's also useful to have a way of taking common matrices and encapsulating them in a way that allows the matrix to be parameterized.

The TransformMatrix is a base class that is is extended by a number of Matrix-creating classes. Instances of TransformMatrix are called by Ren'Py, and return Matrixes. TransformMatrix is well integrated with ATL, allowing for matrixtransform animations.

    transform xrotate:
        matrixtransform RotateMatrix(0.0, 0.0, 0.0)
        linear 4.0 matrixtransform RotateMatrix(360.0, 0.0, 0.0)
        repeat

Subclasses of TransformMatrix are expected to implement the `__call__` method. This method takes:

- An old object to interpolate off of. This object may be of any class, and may be None if no old object exists.
- A value between 0.0 and 1.0, representing the point to interpolate. 0.0 is entirely the old object, and 1.0 is entirely the new object.

## Built-In TransformMatrix Subclasses

The following is the list of TransformMatrix subclasses that are built into Ren'Py.

`OffsetMatrix`(x, y, z)

  A TransformMatrix that returns a matrix that offsets the vertex by a fixed amount.

`RotateMatrix`(x, y, z)

  A TransformMatrix that returns a matrix that rotates the displayable around the origin.

  x, y, z
    The amount to rotate around the origin, in degrees.

  The rotations are applied in order:

  - A clockwise rotation by x degrees in the Y/Z plane.
  - A clockwise rotation by y degrees in the Z/X plane.
  - A clockwise rotation by z degrees in the X/Y plane.

`ScaleMatrix`(x, y, z)

  A TransformMatrix that returns a matrix that scales the displayable.

  x, y, z
    The factor to scale each axis by.

## Transform Properties

The following transform properties are used by the 3D Stage.

> `perspective`, `matrixanchor`, `matrixtransform`, `zpos`, `zzoom`

`matrixanchor`

  Type: | (position, position)
  Default: | (0.5, 0.5)

  This gives the position of the matrix anchor relative to the image. If the variables are floats, this is relative to the size of the child, otherwise it's absolute pixels.

  This sets the location of the (0, 0, 0) point that matrixtransform applies its transform to.

`matrixtransform`

  Type: | None or Matrix or TransformMatrix
  Default: | None

  If not None, this gives a matrix that is used to transform the vertices of the child of the transform. The transformation goes from the coordinates used by the screen to the coordinates used by the child of the transform.

  Interpolations involving this property are only supported when using a TransformMatrix, and when the TransformMatrix values are structurally similar, as described above.

`perspective`

  Type: | True or False or Float or (Float, Float, Float)
  Default: | None

  When applied to a transform, this enables perspective rendering. This takes a triple, giving the near plane, z-distance to the 1:1 plane, and far plane.

  If a single float, the distances to the near and far planes are taken from `config.perspective`. If True, all three values are taken from that variable.

  When perspective is not false, the meaning of the `xpos`, `ypos`, `zpos`, and `rotate` are inverted, providing the effect of positioning the camera rather than the child.

  As the perspective transformation assumes it's aligned with the window, it doesn't make sense to reposition it using `xanchor`, and `yanchor`, or properties that set those, such as `anchor`, `align`, `center`, etc.

`zpos`

  Type: | float
  Default: | 0

  This offsets the child along the z-axis. When perspective is false, this is used directly, otherwise it is multiplied by -1 and used.

  If setting this causes the child to disappear, it's likely that the transform is not being used with a displayable where zpos is False.

`zzoom`

  Type: | bool
  Default: | False

  If this is true, the z-distance to the 1:1 plane (zone) is determined, along with this displayable's zpos. The child is then scaled by (zone - zpos) / zone in the x and y axes.

  The intended use for this is in displaying a background with a negative zpos, which would normally make the background small. Setting this to true means that the background will be displayed at 1:1 size.