### 6.7.2  Normal

Ray-tracing is known for the dramatic way it depicts reflection, refraction and lighting effects. Much of our perception depends on the reflective properties of an object. Ray tracing can exploit this by playing tricks on our perception to make us see complex details that aren't really there.

Suppose you wanted a very bumpy surface on the object. It would be very difficult to mathematically model lots of bumps. We can however simulate the way bumps look by altering the way light reflects off of the surface. Reflection calculations depend on a vector called a surface normal vector. This is a vector which points away from the surface and is perpendicular to it. By artificially modifying (or perturbing) this normal vector you can simulate bumps. This is done by adding an optional ``` normal``` statement.

Note: that attaching a normal pattern does not really modify the surface. It only affects the way light reflects or refracts at the surface so that it looks bumpy.

The syntax is:

```NORMAL:
normal { [NORMAL_IDENTIFIER] [NORMAL_TYPE] [NORMAL_MODIFIER...] }
NORMAL_TYPE:
PATTERN_TYPE Amount |
bump_map { BITMAP_TYPE "bitmap.ext" [BUMP_MAP_MODS...]}
NORMAL_MODIFIER:
PATTERN_MODIFIER | NORMAL_LIST | normal_map { NORMAL_MAP_BODY } |
slope_map{ SLOPE_MAP_BODY } | bump_size Amount |
no_bump_scale Bool | accuracy Float
```

Each of the items in a normal are optional but if they are present, they must be in the order shown. Any items after the NORMAL_IDENTIFIER modify or override settings given in the identifier. If no identifier is specified then the items modify the normal values in the current default texture. The PATTERN_TYPE may optionally be followed by a float value that controls the apparent depth of the bumps. Typical values range from 0.0 to 1.0 but any value may be used. Negative values invert the pattern. The default value if none is specified is 0.5.

There are four basic types of NORMAL_TYPEs. They are block pattern normals, continuous pattern normals, specialized normals and bump maps. They differ in the types of modifiers you may use with them. The pattern type is optionally followed by one or more normal modifiers. In addition to general pattern modifiers such as transformations, turbulence, and warp modifiers, normals may also have a NORMAL_LIST, `slope_map`, ``` normal_map```, and `bump_size` which are specific to normals. See "Pattern Modifiers" for information on general modifiers. The normal-specific modifiers are described in sub-sections which follow. Normal modifiers of any kind apply only to the normal and not to other parts of the texture. Modifiers must be specified last.

Originally POV-Ray had some patterns which were exclusively used for pigments while others were exclusively used for normals. Since POV-Ray 3.0 you can use any pattern for either pigments or normals. For example it is now valid to use `ripples` as a pigment or `wood` as a normal type. The patterns `bumps`, `dents`, ``` ripples```, `waves`, ` wrinkles`, and ``` bump_map``` were once exclusively normal patterns which could not be used as pigments. Because these six types use specialized normal modification calculations they cannot have ` slope_map`, ``` normal_map``` or wave shape modifiers. All other normal pattern types may use them. Because block patterns ` checker`, `hexagon`, `object` and ` brick` do not return a continuous series of values, they cannot use these modifiers either. See "Patterns" for details about specific patterns.

A ` normal` statement is part of a ` texture` specification. However it can be tedious to use a ` texture` statement just to add bumps to an object. Therefore you may attach a normal directly to an object without explicitly specifying that it as part of a texture. For example instead of this:

```  object  {My_Object texture { normal { bumps 0.5 } } }
```

you may shorten it to:

```  object { My_Object normal { bumps 0.5 } }
```

Doing so creates an entire `texture` structure with default `pigment` and `finish` statements just as if you had explicitly typed the full ``` texture {...}``` around it. Normal identifiers may be declared to make scene files more readable and to parameterize scenes so that changing a single declaration changes many values. An identifier is declared as follows.

```NORMAL_DECLARATION:
#declare IDENTIFIER = NORMAL |
#local IDENTIFIER = NORMAL
```

Where IDENTIFIER is the name of the identifier up to 40 characters long and NORMAL is any valid `normal` statement. See "#declare vs. #local" for information on identifier scope.

#### 6.7.2.1  Slope Maps

A `slope_map` is a normal pattern modifier which gives the user a great deal of control over the exact shape of the bumpy features. Each of the various pattern types available is in fact a mathematical function that takes any x, y, z location and turns it into a number between 0.0 and 1.0 inclusive. That number is used to specify where the various high and low spots are. The `slope_map` lets you further shape the contours. It is best illustrated with a gradient normal pattern. Suppose you have...

```  plane{ z, 0
pigment{ White }
}
```

This gives a ramp wave pattern that looks like small linear ramps that climb from the points at x=0 to x=1 and then abruptly drops to 0 again to repeat the ramp from x=1 to x=2. A slope map turns this simple linear ramp into almost any wave shape you want. The syntax is as follows...

```SLOPE_MAP:
slope_map { SLOPE_MAP_BODY }
SLOPE_MAP_BODY:
SLOPE_MAP_IDENTIFIER | SLOPE_MAP_ENTRY...
SLOPE_MAP_ENTRY:
[ Value, <Height, Slope> ]
```

Note: the `[]` brackets are part of the actual SLOPE_MAP_ENTRY. They are not notational symbols denoting optional parts. The brackets surround each entry in the slope map.

There may be from 2 to 256 entries in the map.

Each `Value` is a float value between 0.0 and 1.0 inclusive and each ` <Height`, ``` Slope>``` is a 2 component vector such as <0,1> where the first value represents the apparent height of the wave and the second value represents the slope of the wave at that point. The height should range between 0.0 and 1.0 but any value could be used.

The slope value is the change in height per unit of distance. For example a slope of zero means flat, a slope of 1.0 means slope upwards at a 45 degree angle and a slope of -1 means slope down at 45 degrees. Theoretically a slope straight up would have infinite slope. In practice, slope values should be kept in the range -3.0 to +3.0. Keep in mind that this is only the visually apparent slope. A normal does not actually change the surface.

For example here is how to make the ramp slope up for the first half and back down on the second half creating a triangle wave with a sharp peak in the center.

```  normal {
gradient x       // this is the PATTERN_TYPE
slope_map {
[0   <0, 1>]   // start at bottom and slope up
[0.5 <1, 1>]   // halfway through reach top still climbing
[0.5 <1,-1>]   // abruptly slope down
[1   <0,-1>]   // finish on down slope at bottom
}
}
```

The pattern function is evaluated and the result is a value from 0.0 to 1.0. The first entry says that at x=0 the apparent height is 0 and the slope is 1. At x=0.5 we are at height 1 and slope is still up at 1. The third entry also specifies that at x=0.5 (actually at some tiny fraction above 0.5) we have height 1 but slope -1 which is downwards. Finally at x=1 we are at height 0 again and still sloping down with slope -1.

Although this example connects the points using straight lines the shape is actually a cubic spline. This example creates a smooth sine wave.

```  normal {
gradient x          // this is the PATTERN_TYPE
slope_map {
[0    <0.5, 1>]   // start in middle and slope up
[0.25 <1.0, 0>]   // flat slope at top of wave
[0.5  <0.5,-1>]   // slope down at mid point
[0.75 <0.0, 0>]   // flat slope at bottom
[1    <0.5, 1>]   // finish in middle and slope up
}
}
```

This example starts at height 0.5 sloping up at slope 1. At a fourth of the way through we are at the top of the curve at height 1 with slope 0 which is flat. The space between these two is a gentle curve because the start and end slopes are different. At half way we are at half height sloping down to bottom out at 3/4ths. By the end we are climbing at slope 1 again to complete the cycle. There are more examples in ` slopemap.pov` in the sample scenes.

A `slope_map` may be used with any pattern except ``` brick```, `checker`, `object`, `hexagon`, ``` bumps```, `dents`, ` ripples`, `waves`, ` wrinkles` and ` bump_map`.

You may declare and use slope map identifiers. For example:

```  #declare Fancy_Wave =
slope_map {       // Now let's get fancy
[0.0  <0, 1>]   // Do tiny triangle here
[0.2  <1, 1>]   //  down
[0.2  <1,-1>]   //     to
[0.4  <0,-1>]   //       here.
[0.4  <0, 0>]   // Flat area
[0.5  <0, 0>]   //   through here.
[0.5  <1, 0>]   // Square wave leading edge
[0.6  <1, 0>]   //   trailing edge
[0.6  <0, 0>]   // Flat again
[0.7  <0, 0>]   //   through here.
[0.7  <0, 3>]   // Start scallop
[0.8  <1, 0>]   //   flat on top
[0.9  <0,-3>]   //     finish here.
[0.9  <0, 0>]   // Flat remaining through 1.0
}
object{ My_Object
pigment { White }
normal {
wood
slope_map { Fancy_Wave }
}
}
```
##### 6.7.2.1.1  Normals, Accuracy

Surface normals that use patterns that were not designed for use with normals (anything other than bumps, dents, waves, ripples, and wrinkles) uses a `slope_map` whether you specify one or not. To create a perturbed normal from a pattern, POV-Ray samples the pattern at four points in a pyramid surrounding the desired point to determine the gradient of the pattern at the center of the pyramid. The distance that these points are from the center point determines the accuracy of the approximation. Using points too close together causes floating-point inaccuracies. However, using points too far apart can lead to artefacts as well as smoothing out features that should not be smooth.

Usually, points very close together are desired. POV-Ray currently uses a delta or accuracy distance of 0.02. Sometimes it is necessary to decrease this value to get better accuracy if you are viewing a close-up of the texture. Other times, it is nice to increase this value to smooth out sharp edges in the normal (for example, when using a 'solid' crackle pattern). For this reason, a new property, `accuracy`, has been added to normals. It only makes a difference if the normal uses a `slope_map` (either specified or implied).

You can specify the value of this accuracy (which is the distance between the sample points when determining the gradient of the pattern for slope_map) by adding `accuracy <float>` to your normal. For all patterns, the default is 0.02.

#### 6.7.2.2  Normal Maps and Normal Lists

Most of the time you will apply single normal pattern to an entire surface but you may also create a pattern or blend of normals using a ``` normal_map```. The syntax for a `normal_map` is identical to a `pigment_map` except you specify a ` normal` in each map entry. The syntax for `normal_map` is as follows:

```NORMAL_MAP:
normal_map { NORMAL_MAP_BODY }
NORMAL_MAP_BODY:
NORMAL_MAP_IDENTIFIER | NORMAL_MAP_ENTRY...
NORMAL_MAP_ENTRY:
[ Value NORMAL_BODY ]
```

Where `Value` is a float value between 0.0 and 1.0 inclusive and each NORMAL_BODY is anything which can be inside a `normal{...}` statement. The `normal` keyword and `{}` braces need not be specified.

Note: that the `[]` brackets are part of the actual NORMAL_MAP_ENTRY. They are not notational symbols denoting optional parts. The brackets surround each entry in the normal map.

There may be from 2 to 256 entries in the map.

For example

```  normal {
gradient x       //this is the PATTERN_TYPE
normal_map {
[0.3  bumps scale 2]
[0.3  dents]
[0.6  dents]
[0.9  marble turbulence 1]
}
}
```

When the `gradient x` function returns values from 0.0 to 0.3 then the scaled bumps normal is used. From 0.3 to 0.6 dents pattern is used. From 0.6 up to 0.9 a blend of dents and a turbulent marble is used. From 0.9 on up only the turbulent marble is used.

Normal maps may be nested to any level of complexity you desire. The normals in a map may have slope maps or normal maps or any type of normal you want.

A normal map is also used with the `average` normal type. See "Average" for details.

Entire normals in a normal list may also be used with the block patterns such as `checker`, `hexagon` and `brick`. For example...

```  normal {
checker
normal { gradient x scale .2 }
normal { gradient y scale .2 }
}
```

Note: in the case of block patterns the `normal` wrapping is required around the normal information.

You may not use ` normal_map` or individual normals with a ``` bump_map```. See section "Texture Maps" for an alternative way to do this.

You may declare and use normal map identifiers but the only way to declare a normal block pattern list is to declare a normal identifier for the entire normal.

#### 6.7.2.3  Bump Maps

When all else fails and none of the above normal pattern types meets your needs you can use a `bump_map` to wrap a 2-D bit-mapped bump pattern around your 3-D objects.

Instead of placing the color of the image on the shape like an ``` image_map``` a `bump_map` perturbs the surface normal based on the color of the image at that point. The result looks like the image has been embossed into the surface. By default, a bump map uses the brightness of the actual color of the pixel. Colors are converted to gray scale internally before calculating height. Black is a low spot, white is a high spot. The image's index values may be used instead (see section "Use_Index and Use_Color" below).

##### 6.7.2.3.1  Specifying a Bump Map

The syntax for a `bump_map` is:

```BUMP_MAP:
normal
{
bump_map
{
BITMAP_TYPE "bitmap.ext"
[BUMP_MAP_MODS...]
}
[NORMAL_MODFIERS...]
}
BITMAP_TYPE:
gif | tga | iff | ppm | pgm | png | jpeg | tiff | sys
BUMP_MAP_MOD:
map_type Type | once | interpolate Type | use_color |
use_colour | bump_size Value
```

After the required BITMAP_TYPE keyword is a string expression containing the name of a bitmapped bump file of the specified type. Several optional modifiers may follow the file specification. The modifiers are described below.

Note: earlier versions of POV-Ray allowed some modifiers before the BITMAP_TYPE but that syntax is being phased out in favor of the syntax described here.

Note: `sys` format is a system-specific format such as BMP for Windows or Pict for Macintosh.

Filenames specified in the `bump_map` statements will be searched for in the home (current) directory first and, if not found, will then be searched for in directories specified by any `+L` or ``` Library_Path``` options active. This would facilitate keeping all your bump maps files in a separate subdirectory and giving a ``` Library_Path``` option to specify where your library of bump maps are. See "Library Paths" for details.

By default, the bump pattern is mapped onto the x-y-plane. The bump pattern is projected onto the object as though there were a slide projector somewhere in the -z-direction. The pattern exactly fills the square area from (x,y) coordinates (0,0) to (1,1) regardless of the pattern's original size in pixels. If you would like to change this default you may translate, rotate or scale the pigment or texture to map it onto the object's surface as desired. If you would like to change this default orientation you may translate, rotate or scale the pigment or texture to map it onto the object's surface as desired.

The file name is optionally followed by one or more BITMAP_MODIFIERS. The `bump_size`, ` use_color` and ` use_index` modifiers are specific to bump maps and are discussed in the following sections. See section "Bitmap Modifiers" for the generic bitmap modifiers `map_type`, `once` and ` interpolate` described in "Bitmap Modifiers"

##### 6.7.2.3.2  Bump_Size

The relative bump size can be scaled using the `bump_size` modifier. The bump size number can be any number other than 0 but typical values are from about 0.1 to as high as 4.0 or 5.0.

```  normal {
bump_map {
gif "stuff.gif"
bump_size 5.0
}
}
```

Originally `bump_size` could only be used inside a bump map but it can now be used with any normal. Typically it is used to override a previously defined size. For example:

```  normal {
My_Normal   //this is a previously defined normal identifier
bump_size 2.0
}
```
##### 6.7.2.3.3  Use_Index and Use_Color

Usually the bump map converts the color of the pixel in the map to a gray scale intensity value in the range 0.0 to 1.0 and calculates the bumps based on that value. If you specify `use_index`, the bump map uses the color's palette number to compute as the height of the bump at that point. So, color number 0 would be low and color number 255 would be high (if the image has 256 palette entries). The actual color of the pixels doesn't matter when using the index. This option is only available on palette based formats. The `use_color` keyword may be specified to explicitly note that the color methods should be used instead. The alternate spelling `use_colour` is also valid. These modifiers may only be used inside the `bump_map` statement.

#### 6.7.2.4  Scaling normals

When scaling a normal, or when scaling an object after a normal is applied to it, the depth of the normal is affected by the scaling. This is not always wanted. If you want to turn off bump scaling for a texture or normal, you can do this by adding the keyword `no_bump_scale` to the texture's or normal's modifiers. This modifier will get passed on to all textures or normals contained in that texture or normal. Think of this like the way no_shadow gets passed on to objects contained in a CSG.

It is also important to note that if you add `no_bump_scale` to a normal or texture that is contained within another pattern (such as within a `texture_map` or `normal_map`), then the only scaling that will be ignored is the scaling of that texture or normal. Scaling of the parent texture or normal or of the object will affect the depth of the bumps, unless `no_bump_scale` is specified at the top-level of the texture (or normal, if the normal is not wrapped in a texture).