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Minecraft:Density function: Difference between revisions

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== Marker functions ==
== Marker functions ==
=== interpolated ===
=== {{cd|cache}} ===
Interpolates at each block in one cell based on the input density function value of some cells around. The size of each cell is <code>size_horizontal * 4</code> and <code>size_vertical * 4</code>. Used often in combination with <code>flat_cache</code>.
If this density function is referenced twice, it is only computed once per block position.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache</code>).
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input to be cached.
</div>
 
=== {{cd|interpolated}} ===
{{until|JE 26.4}}
 
Interpolates at each block in one cell based on the input density function value of some cells around. The size of each cell is <code>size_horizontal * 4</code> and <code>size_vertical * 4</code>.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>interpolated</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>interpolated</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be interpolated.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input to be interpolated.
** {{nbt|int|cell_size_xz}}: Size in blocks of the interpolation grid cells on the X and Z axes. The number must not be negative.
** {{nbt|int|cell_size_y}}: Size in blocks of the interpolation grid cells on the Y axis. The number must not be negative.
</div>
</div>


=== flat_cache ===
=== {{cd|upscale}} ===
Calculate the value per 4×4 column (Value at each block in one column is the same). And it is calculated only once per column, at Y=0. Used often in combination with <code>interpolated</code>.
Samples the input function at a reduced resolution and upscales on each axis with the specified modes. Modes that require more samples will generally perform worse. Upscaling is peformed by axis in order of Z, X, then Y.{{upcoming|JE 26.4}}
 
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{nbt|string|type}}: The ID of the density function type (in this case, <code>upscale</code>).
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input to sample.
** {{nbt|int-array|point}}: {{cd|[x, y, z]}}; the configuration for this axis.
*** {{nbt|string|mode}}: one of:
**** {{nbt|int|nearest_neighbor}}: Value is discontinuous across cell boundaries, with the gradient always at 0. The values at cell vertices will always be equal to the cell value. One sample per axis.
**** {{nbt|int|interpolate_linear}}: Value is continuous, and the gradient is content with a cell but discontinuous across cell boundaries. The values at cell vertices will always be equal to the cell value. Two samples per axis.
**** {{nbt|int|interpolate_cosine}}: Value and gradient are continuous, and the gradient is 0 at cell boundaries. The values at cell vertices will always be equal to the cell value. Two samples per axis.
**** {{nbt|int|interpolate_cubic}}: Value and gradient are continuous. The values at cell vertices will always be equal to the cell value. Four samples per axis.
**** {{nbt|int|b_spline_cubic}}: Value and gradient are continuous. The values at cell vertices do not necessarily need to equal to the cell value. Four samples per axis.
*** {{nbt|int|cell_size}}: The size of each upscaling cell. Value between 1 and 64, inclusive.
</div>
 
== Noise sampling functions ==
These density functions are used to sample [[Minecraft:Custom noise|noises]].
 
=== {{cd|noise}} ===
Samples a noise.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>noise</code>).
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|double|xz_scale}}: Scales the X and Z before sampling.
** {{Nbt|double|y_scale}}: Scales the Y before sampling.
** {{nbt|double|shift_x}}: Optional; A domain warp to apply on X. If not specified, no warping will be applied (equivalent to 0).
** {{nbt|double|shift_y}}: Optional; A domain warp to apply on Y. If not specified, no warping will be applied (equivalent to 0).
** {{nbt|double|shift_z}}: Optional; A domain warp to apply on Z. If not specified, no warping will be applied (equivalent to 0).
</div>
 
=== {{cd|old_blended_noise}} ===
Samples a legacy noise. {{Info needed}}
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>flat_cache</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>old_blended_noise</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
** {{Nbt|double|xz_scale}}: Value between 0.001 and 1000.0 (both inclusive).
** {{Nbt|double|y_scale}}: Value between 0.001 and 1000.0 (both inclusive).
** {{Nbt|double|xz_factor}}: Value between 0.001 and 1000.0 (both inclusive).
** {{Nbt|double|y_factor}}: Value between 0.001 and 1000.0 (both inclusive).
** {{Nbt|double|smear_scale_multiplier}}: Value between 1.0 and 8.0 (both inclusive).
</div>
</div>


=== cache_2d ===
=== {{cd|shift}} ===
Only computes the input density once per horizontal position.
Samples a noise at <code>(x/4, y/4, z/4)</code>, then multiplies it by 4.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache_2d</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
</div>


=== cache_once ===
=== {{cd|shift_a}} ===
If this density function is referenced twice, it is only computed once per block position.
Samples a noise at <code>(x/4, 0, z/4)</code>, then multiplies it by 4.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache_once</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift_a</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
</div>


=== cache_all_in_cell ===
=== {{cd|shift_b}} ===
Used by the game onto <code>final_density</code> and should not be referenced in data packs.
Samples a noise at <code>(z/4, x/4, 0)</code>, then multiplies it by 4.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache_all_in_cell</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift_b</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
</div>


== Mapped density functions ==
== Mathematical density functions ==
=== abs ===
These density functions are used to perform mathematical operations.
 
=== {{cd|abs}} ===
Calculates the absolute value of the input density function.
Calculates the absolute value of the input density function.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>abs</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>abs</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
</div>
 
=== {{cd|add}} ===
Adds two density functions together.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>add</code>).
** {{Nbt|string}}{{Nbt|double|left}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double|right}}: {{json ref/density function}} &mdash; The second input of the calculation.
</div>
</div>


=== square ===
=== {{cd|ceil}} ===
Squares the input. (<code>x^2</code>)
Rounds the input value to positive infinity.
 
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>square</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>ceil</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to round.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|multiple}}: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.
</div>
</div>


=== cube ===
=== {{cd|clamp}} ===
Cubes the input (<code>x^3</code>).
Clamps the input between two values.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cube</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>clamp</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: One density function &mdash; The input to clamp.
** {{Nbt|double|min}}: The lower bound. Value between −1000000.0 and 1000000.0 (both inclusive).
** {{Nbt|double|max}}: The upper bound. Value between −1000000.0 and 1000000.0 (both inclusive).
</div>
</div>


=== half_negative ===
=== {{cd|constant}} ===
If the input is negative, returns half of the input. Otherwise returns the input. (<code>x < 0 ? x/2 : x</code>)
A constant value.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>half_negative</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>constant</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|double|argument|value}}: A constant value. Value between −1000000.0 and 1000000.0 (both inclusive).
</div>
</div>


=== quarter_negative ===
=== {{cd|cube}} ===
If the input is negative, returns a quarter of the input. Otherwise returns the input. (<code>x < 0 ? x/4 : x</code>)
Cubes the input (<code>x^3</code>).
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>quarter_negative</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cube</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
</div>
</div>


=== squeeze ===
=== {{cd|div}} ===
First clamps the input between −1 and 1, then transforms it using x/2 - x*x*x/24.
Performs division between two arguments.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>squeeze</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>div</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|left}} &mdash; The left-hand side of the operation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|right}} &mdash; The right-hand side of the operation.
</div>
</div>


=== invert ===
=== {{cd|floor}} ===
Inverts the input (<code>1/x</code>).
Rounds the input value to negative infinity.
 
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>invert</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>floor</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to round.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|multiple}}: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.
</div>
</div>


== Functions with two arguments ==
=== {{cd|log}} ===
=== add ===
Computes the natural logarithm of the given input.
Adds two density functions together.
 
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>add</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>log</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument1}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function for which to compute the natural logarithm.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument2}}: {{json ref/density function}} &mdash; The second input of the calculation.
</div>
</div>


=== mul ===
=== {{cd|mul}} ===
Multiplies two inputs.
Multiplies two inputs.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>mul</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>mul</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument1}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double|left}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument2}}: {{json ref/density function}} &mdash; The second input of the calculation.
** {{Nbt|string}}{{Nbt|double|right}}: {{json ref/density function}} &mdash; The second input of the calculation.
</div>
</div>


=== min ===
=== {{cd|min}} ===
Returns the minimum of two inputs.
Returns the minimum of two inputs.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>min</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>min</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument1}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double|left}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument2}}: {{json ref/density function}} &mdash; The second input of the calculation.
** {{Nbt|string}}{{Nbt|double|right}}: {{json ref/density function}} &mdash; The second input of the calculation.
</div>
</div>


=== max ===
=== {{cd|max}} ===
Returns the maximum of two inputs.
Returns the maximum of two inputs.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>max</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>max</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument1}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double|left}}: {{json ref/density function}} &mdash; The first input of the calculation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument2}}: {{json ref/density function}} &mdash; The second input of the calculation.
** {{Nbt|string}}{{Nbt|double|right}}: {{json ref/density function}} &mdash; The second input of the calculation.
</div>
</div>


== Other density functions ==
=== {{cd|negate}} ===
=== blend_alpha ===
Negates the input.
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{nbt|string|type}}: The ID of the density function type (in this case, <code>negate</code>).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to negate.
</div>
 
=== {{cd|pow}} ===
Raises the given base value to an exponent.
 
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>pow</code>).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|base}}: the base value (Density Function).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|exponent}}: the exponent (Density Function).
</div>
 
=== {{cd|reciprocal}} ===
Inverts the input (<code>1/x</code>).
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>reciprocal</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input of the calculation.
</div>
 
=== {{cd|round}} ===
Rounds the input value to to the nearest integer (ties round up).
 
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>round</code>).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to round.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|multiple}}: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.
</div>
 
=== {{cd|sub}} ===
Performs subtraction between two arguments.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>sub</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|left}} &mdash; The left-hand side of the operation.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|right}} &mdash; The right-hand side of the operation.
</div>
 
=== {{cd|sign}} ===
Computes the sign of the given input.  If positive, it returns as 1. If the input is 0, it returns 0. If negative, it returns as -1.
 
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>sign</code>).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function for which to compute the sign.
</div>
 
=== {{cd|sqrt}} ===
Computes the square root of the given input.
 
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_alpha</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>sqrt</code>).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function for which to compute the square root.
</div>
</div>


=== blend_offset ===
=== {{cd|square}} ===
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
Squares the input. (<code>x^2</code>)
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_offset</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>square</code>).
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
</div>
</div>


=== blend_density ===
=== {{cd|truncate}} ===
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
Rounds the input value to 0.
 
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_density</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>truncate</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The desired density of new chunks.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to round.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|multiple}}: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.
</div>
</div>


=== beardifier ===
== Mapped density functions ==
Adds beards for structures (see the <code>terrain_adaptation</code> field in [[Minecraft:Structure/JSON format|structures]]). Its value is added to the <code>final_density</code> in noise setting by the game. Should not be referenced in data packs.
These density functions map a set of values onto another set of values.
 
=== {{cd|gradient}} ===
[[File:Gradient tiling.png|thumb|Demonstration of the different tiling options for the {{cd|gradient}} density function, using both an input range of -100 to 100 and an output range of -1 to 1.]]
Clamps the given coordinate and maps the gradient to a range.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>beardifier</code>).
** {{nbt|string|type}}: The ID of the density function type (in this case, <code>gradient</code>).
** {{nbt|string|axis}}: {{cd|x}}, {{cd|y}}. or {{cd|z}}: The axis over which to define the gradient .
** {{nbt|string|tiling}}: How the density function handles values outside the specified coordinate range. 3 options:
*** <code>clamp_to_edge</code>: outside the gradient boundaries, the value at the nearest boundary will be used.
*** <code>repeat</code>: The gradient will be repeated outside its boundaries.
*** <code>mirrored_repeat</code>: The gradient will be repeated as such that odd repetitions are mirrored, ensuring continuity between repetitions.
** {{nbt|int|from_coordinate}}: The coordinate at which the gradient starts.
** {{nbt|int|to_coordinate}}: The coordinate at which the gradient ends. It must not equal {{cd|from_coordinate}}.
** {{nbt|float|from_value}}: The value at which the gradient starts.
** {{nbt|float|to_value}}: The value at which the gradient ends.
</div>
</div>


=== old_blended_noise ===
=== {{cd|lerp}} ===
Samples a legacy noise. {{Info needed}}
Performs (unclamped) linear interpolation between two arguments based on an alpha. The returned value is: <code>first*(1-alpha) + second*alpha</code>
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>old_blended_noise</code>).
** {{nbt|string|type}}: The ID of the density function type (in this case, <code>lerp</code>).
** {{Nbt|double|xz_scale}}: Value between 0.001 and 1000.0 (both inclusive).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|alpha}}: Density function representing the interpolation factor (e.g. 0 = first, 1 = second). Any value outside of {{cd|[0; 1]}} will extrapolate.
** {{Nbt|double|y_scale}}: Value between 0.001 and 1000.0 (both inclusive).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|first}}: Density Function to use at {{cd|<nowiki>alpha=0</nowiki>}}.
** {{Nbt|double|xz_factor}}: Value between 0.001 and 1000.0 (both inclusive).
** {{nbt|string}}{{nbt|double}}{{nbt|compound|second}}: Density Function to use at {{cd|<nowiki>alpha=1</nowiki>}}.
** {{Nbt|double|y_factor}}: Value between 0.001 and 1000.0 (both inclusive).
** {{Nbt|double|smear_scale_multiplier}}: Value between 1.0 and 8.0 (both inclusive).
</div>
</div>


=== noise ===
=== {{cd|squeeze}} ===
Samples a [[Minecraft:Custom_noise|noise]].
First clamps the input between −1 and 1, then transforms it using x/2 - x*x*x/24.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>noise</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>squeeze</code>).
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|double|xz_scale}}: Scales the X and Z before sampling.
** {{Nbt|double|y_scale}}: Scales the Y before sampling.
</div>
</div>


=== end_islands ===
=== {{cd|spline}} ===
Samples at current position using a noise algorithm used for end islands. Its minimum value is −0.84375 and its maximum value is 0.5625.
Computes a cubic spline.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>end_islands</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>spline</code>).
** {{Nbt|float}}{{Nbt|compound|spline}}: The spline. Can be either a number or an object.
*** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|coordinate}}: {{json ref/density function}} &mdash; Input determining the location on the spline.
*** {{Nbt|list|points}}: (Cannot be empty) List of points of the cubic spline.
**** {{Nbt|compound}}: A point of the cubic spline.
***** {{Nbt|float|location}}: The location of this point.
***** {{Nbt|float}}{{Nbt|compound|value}}: The value of this point. Can be either a number or a spline object.
***** {{Nbt|float|derivative}}: The slope at this point.
</div>
</div>


=== weird_scaled_sampler ===
== Conditional density functions ==
{{in development|section=1|JE||26.2|removed=1}}
These density functions are used to apply "if-then" logic.
According to the input value, scales and enhances (or weakens) some regions of the specified noise, and then returns the absolute value.
 
=== {{cd|half_negative}} ===
If the input is negative, returns half of the input. Otherwise returns the input. (<code>x < 0 ? x/2 : x</code>)
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>weird_scaled_sampler</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>half_negative</code>).
** {{Nbt|string|rarity_value_mapper}}: Can be <code>type_1</code>（The minimum scale is 0.75, and the maximum is 2.0）or <code>type_2</code>（The minimum scale is 0.5, and the maximum is 3.0.)
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|input}}: The input density function. Can be an ID of a density function, or a density function in the form of a JSON object or a constant number.
</div><!--
TYPE2
if (d < −0.75) {
return 0.5;
} else if (d < −0.5) {
return 0.75;
} else if (d < 0.5) {
return 1.0;
} else {
return d < 0.75 ? 2.0 : 3.0;
}


TYPE1
=== {{cd|interval_select}} ===
if (d < −0.5) {
Selects between a number of density functions based on an input density function and a set of threshold values.
return 0.75;
<div class="treeview">
} else if (d < 0.0) {
* {{nbt|compound}}: Root object.
return 1.0;
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>interval_select</code>).
} else {
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: Density Function to be compared with any given {{cd|thresholds}}.
return d < 0.5 ? 1.5 : 2.0;
** {{nbt|list|thresholds}}: (List of Floats) The threshold values to compare {{cd|input}} with.
}
*** If the input value is less than the threshold values, the result of {{cd|functions[i]}} will be selected.
-->
*** If the input value is greater than the last threshold value, the last function will be selected.
*** There must be one fewer {{cd|thresholds}} than {{cd|functions}}.
** {{nbt|list|functions}}: The resulting functions (at least two) to be selected from.
*** There must be one more element in {{cd|functions}} than {{cd|thresholds}}.
</div>


=== shifted_noise ===
=== {{cd|quarter_negative}} ===
Similar to <code>noise</code>, but first shifts the input coordinates.
If the input is negative, returns a quarter of the input. Otherwise returns the input. (<code>x < 0 ? x/4 : x</code>)
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shifted_noise</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>quarter_negative</code>).
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The input of the calculation.
** {{Nbt|double|xz_scale}}: Scales the X and Z before sampling.
** {{Nbt|double|y_scale}}: Scales the Y before sampling.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_x}}: {{json ref/density function}} &mdash; offset of the position in the X direction.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_y}}: {{json ref/density function}} &mdash; offset of the position in the Y direction.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_z}}: {{json ref/density function}} &mdash; offset of the position in the Z direction.
</div>
</div>


=== range_choice ===
=== {{cd|range_choice}} ===
Computes the input value, and depending on that result returns one of two other density functions. Basically an if-then-else statement.
Computes the input value, and depending on that result returns one of two other density functions. Basically an if-then-else statement.
<div class="treeview">
<div class="treeview">
Line 269: Line 398:
</div>
</div>


=== shift_a ===
== Other density functions ==
Samples a noise at <code>(x/4, 0, z/4)</code>, then multiplies it by 4.
=== {{cd|beardifier}} ===
Adds beards for structures (see the <code>terrain_adaptation</code> field in [[Minecraft:Structure/JSON format|structures]]). Its value is added to the <code>final_density</code> in noise setting by the game. Should not be referenced in data packs.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift_a</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>beardifier</code>).
** {{Nbt|string|argument}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
</div>


=== shift_b ===
=== {{cd|blend_alpha}} ===
Samples a noise at <code>(z/4, x/4, 0)</code>, then multiplies it by 4.
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift_b</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_alpha</code>).
** {{Nbt|string|argument}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
</div>
</div>


=== shift ===
=== {{cd|blend_density}} ===
Samples a noise at <code>(x/4, y/4, z/4)</code>, then multiplies it by 4.
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shift</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_density</code>).
** {{Nbt|string|argument}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|string}}{{Nbt|double|input}}: {{json ref/density function}} &mdash; The desired density of new chunks.
</div>
</div>


=== clamp ===
=== {{cd|blend_offset}} ===
Clamps the input between two values.
Used in vanilla for smooth transition to chunks generated in old versions.{{Info needed}}
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>clamp</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>blend_offset</code>).
** {{Nbt|double}}{{Nbt|compound|input}}: One '''density function''' (a new {{Nbt|double}}{{Nbt|compound}} density function definition, an {{Nbt|string|}}[[Minecraft:resource location|ID]] is not allowed here<ref>{{cite bug|MC|252814|Clamp density function takes a direct input and doesn't allow a reference|date=June 11, 2022}}</ref>) &mdash; The input to clamp.
** {{Nbt|double|min}}: The lower bound. Value between −1000000.0 and 1000000.0 (both inclusive).
** {{Nbt|double|max}}: The upper bound. Value between −1000000.0 and 1000000.0 (both inclusive).
</div>
</div>


=== spline ===
=== {{cd|distance_to_point}} ===
Computes a cubic spline.
[[File:Distance to point options.png|thumb|Demonstration of the different metric options for the {{cd|distance_to_point}} density function, using the distance from the point (0, 0).]]
<div class="treeview">
Computes the distance to a fixed point using the specified distance function.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>spline</code>).
** {{Nbt|float}}{{Nbt|compound|spline}}: The spline. Can be either a number or an object.
*** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|coordinate}}: {{json ref/density function}} &mdash; Input determining the location on the spline.
*** {{Nbt|list|points}}: (Cannot be empty) List of points of the cubic spline.
**** {{Nbt|compound}}: A point of the cubic spline.
***** {{Nbt|float|location}}: The location of this point.
***** {{Nbt|float}}{{Nbt|compound|value}}: The value of this point. Can be either a number or a spline object.
***** {{Nbt|float|derivative}}: The slope at this point.
</div>


=== constant ===
A constant value.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>constant</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>distance_to_point</code>).
** {{Nbt|double|argument}}: A constant value. Value between −1000000.0 and 1000000.0 (both inclusive).
** {{nbt|int-array|point}}: {{cd|[x, y, z]}}; the point to compute distance to
** {{nbt|string|metric}}:
*** {{nbt|string|euclidean}}: (i.e. {{cd|sqrt(dx^2 + dy^2 + dz^2)}})
*** {{nbt|string|euclidean_squared}}: (i.e. {{cd|dx^2 + dy^2 + dz^2}})
*** {{nbt|string|manhattan}}: (i.e. {{cd|abs(dx) + abs(dy) + abs(dz)}})
*** {{nbt|string|chebyshev}}: (i.e. {{cd|max(abs(dx), abs(dy), abs(dz))}})
</div>
</div>


=== y_clamped_gradient ===
=== {{cd|end_outer_islands}} ===
Clamps the Y coordinate between <code>from_y</code> and <code>to_y</code> and then linearly maps it to a range.
Samples at current position using a noise algorithm used for end islands. Its minimum value is −0.84375 and its maximum value is 0.5625.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>y_clamped_gradient</code>).
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>end_outer_islands</code>).
** {{Nbt|int|from_y}}: The value to be mapped to <code>from_value</code>. Value between −4064 and 4062 (both inclusive).
** {{Nbt|int|to_y}}: The value to be mapped to <code>to_value</code>. Value between −4064 and 4062 (both inclusive).
** {{Nbt|double|from_value}}: The value to map <code>from_y</code> to. Value between −1000000.0 and 1000000.0 (both inclusive).
** {{Nbt|double|to_value}}: The value to map <code>to_y</code> to. Value between −1000000.0 and 1000000.0 (both inclusive).
</div>
</div>


=== find_top_surface ===
=== {{cd|find_top_surface}} ===
Scans through a column of an input density and returns the topmost y-level that is above 0. If no such position exists withing the bounds, the {{Nbt|int|lower_bound}} is returned.
Scans through a column of an input density and returns the topmost y-level that is above 0. If no such position exists within the bounds, the {{Nbt|int|lower_bound}} is returned.
<div class="treeview">
<div class="treeview">
* {{nbt|compound}}: Root object.
* {{nbt|compound}}: Root object.
Line 345: Line 459:
** {{Nbt|int|lower_bound}}: The y-level to stop the scan.
** {{Nbt|int|lower_bound}}: The y-level to stop the scan.
** {{Nbt|int|cell_height}}: The resolution of the scan. E.g. if set to <code>4</code>, then only every 4th block is checked.
** {{Nbt|int|cell_height}}: The resolution of the scan. E.g. if set to <code>4</code>, then only every 4th block is checked.
</div>
=== {{cd|ore_vein}} ===
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>ore_vein</code>).
** {{nbt|string|ore_block}}: The ore block to place.
** {{nbt|string|raw_ore_block}}: The raw ore block to place.
** {{nbt|string|filler_block}}: The filler block to place.
** {{nbt|float|raw_ore_chance}}: The probability for a raw ore block to be placed instead of an ore block. Value between 0 and 1 (inclusive).
** {{nbt|int|density}}: The probability for the ore vein to replace a block. If the value is 0 or lower, no block will be replaced.
** {{nbt|int|richness}}: The probability for an ore block or a raw ore block to be placed, as opposed to {{cd|filler_block}}. If the value is 0 or lower, all blocks will be the filler block. If the value is 1 or greater, no blocks will be the filler block.
** {{nbt|int|filler_gap}}: Overrides {{cd|richness}}; if the value is positive, {{cd|filler_block}} will always be placed.
</div>
=== {{cd|slice}} ===
Removes a dimension from the input domain by taking a "slice" along an axis with a specific coordinate (e.g. with the axis equaling y and the coordinate of 0, a slice will be taken along the XZ plane, with all values sampled at y=0).
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>slice</code>).
** {{nbt|string|axis}}: {{cd|x}}, {{cd|y}}, or {{cd|z}}; the axis to remove.
** {{nbt|int|coordinate}}: The fixed coordinate to be passed to the input function.
** {{nbt|string}}{{nbt|double}}{{nbt|compound|input}}: The input function.
</div>
</div>


Line 350: Line 489:
{{outdated|section=1}}
{{outdated|section=1}}


=== slide ===
=== {{cd|cache_2d}} ===
Removed in [[Minecraft:26.3-snap10]]
 
Only computes the input density once per horizontal position.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache_2d</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
</div>
 
=== {{cd|cache_all_in_cell}} ===
Removed in [[Minecraft:26.3-snap10]]
 
Used by the game onto <code>final_density</code> and should not be referenced in data packs.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>cache_all_in_cell</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
</div>
 
=== {{cd|flat_cache}} ===
Removed in [[Minecraft:26.3-snap10]]
 
Calculate the value per 4×4 column (Value at each block in one column is the same). And it is calculated only once per column, at Y=0. Used often in combination with <code>interpolated</code>.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>flat_cache</code>).
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|argument}}: {{json ref/density function}} &mdash; The input to be cached.
</div>
 
=== {{cd|shifted_noise}} ===
Removed in [[Minecraft:26.3-snap10]]
 
Similar to <code>noise</code>, but first shifts the input coordinates.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>shifted_noise</code>).
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|double|xz_scale}}: Scales the X and Z before sampling.
** {{Nbt|double|y_scale}}: Scales the Y before sampling.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_x}}: {{json ref/density function}} &mdash; offset of the position in the X direction.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_y}}: {{json ref/density function}} &mdash; offset of the position in the Y direction.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|shift_z}}: {{json ref/density function}} &mdash; offset of the position in the Z direction.
</div>
 
=== {{cd|slide}} ===
Removed in [[Minecraft:22w12a]]
Removed in [[Minecraft:22w12a]]
<div class="treeview">
<div class="treeview">
Line 373: Line 557:
</div>
</div>


=== terrain_shaper_spline ===
=== {{cd|terrain_shaper_spline}} ===
Removed in [[Minecraft:22w11a]]
Removed in [[Minecraft:22w11a]]


Line 387: Line 571:
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|weirdness}}: {{json ref/density function}}
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|weirdness}}: {{json ref/density function}}
</div>
</div>
=== {{cd|weird_scaled_sampler}} ===
Removed in [[Minecraft:26.2-snap5]]
According to the input value, scales and enhances (or weakens) some regions of the specified noise, and then returns the absolute value.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>weird_scaled_sampler</code>).
** {{Nbt|string|rarity_value_mapper}}: Can be <code>type_1</code>（The minimum scale is 0.75, and the maximum is 2.0）or <code>type_2</code>（The minimum scale is 0.5, and the maximum is 3.0.)
** {{Nbt|string|noise}}: {{json ref|noise|Custom noise}} &mdash; The noise to sample.
** {{Nbt|string}}{{Nbt|double}}{{Nbt|compound|input}}: The input density function. Can be an ID of a density function, or a density function in the form of a JSON object or a constant number.
</div>
=== {{cd|y_clamped_gradient}} ===
Removed in [[Minecraft:26.3-snap6]]
Clamps the Y coordinate between <code>from_y</code> and <code>to_y</code> and then linearly maps it to a range.
<div class="treeview">
* {{nbt|compound}}: Root object.
** {{Nbt|string|type}}: The ID of the density function type (in this case, <code>y_clamped_gradient</code>).
** {{Nbt|int|from_y}}: The value to be mapped to <code>from_value</code>. Value between −4064 and 4062 (both inclusive).
** {{Nbt|int|to_y}}: The value to be mapped to <code>to_value</code>. Value between −4064 and 4062 (both inclusive).
** {{Nbt|double|from_value}}: The value to map <code>from_y</code> to. Value between −1000000.0 and 1000000.0 (both inclusive).
** {{Nbt|double|to_value}}: The value to map <code>to_y</code> to. Value between −1000000.0 and 1000000.0 (both inclusive).
</div>
<!--
TYPE2
if (d < −0.75) {
return 0.5;
} else if (d < −0.5) {
return 0.75;
} else if (d < 0.5) {
return 1.0;
} else {
return d < 0.75 ? 2.0 : 3.0;
}
TYPE1
if (d < −0.5) {
return 0.75;
} else if (d < 0.0) {
return 1.0;
} else {
return d < 0.5 ? 1.5 : 2.0;
}
-->


== History ==
== History ==
Line 397: Line 627:
Added fields to {{cd|old_blended_noise}} density function: xz_scale, y_scale, xz_factor, y_factor, and smear_scale_multiplier.}}
Added fields to {{cd|old_blended_noise}} density function: xz_scale, y_scale, xz_factor, y_factor, and smear_scale_multiplier.}}
|{{HistoryLine||1.21.9|dev=25w31a|Added density functions {{cd|minecraft:find_top_surface}} and {{cd|minecraft:invert}}.}}
|{{HistoryLine||1.21.9|dev=25w31a|Added density functions {{cd|minecraft:find_top_surface}} and {{cd|minecraft:invert}}.}}
|{{HistoryLine||26.2|dev=snap1|Density function {{cd|minecraft:clamp}} can now take a density function ID as an input.}}
|{{HistoryLine|||dev=snap5|Added density function {{cd|minecraft:interval_select}}.|Removed density function {{cd|minecraft:weird_scale_sampler}}. Its functionality has been replaced with {{cd|interval_select}}.}}
|{{HistoryLine||26.3|dev=snap4|Added the following density functions:
* {{cd|ceil}}
* {{cd|div}}
* {{cd|floor}}
* {{cd|negate}}
* {{cd|lerp}}
* {{cd|round}}
* {{cd|sub}}
* {{cd|truncate}}
|{{cd|invert}} has been renamed to {{cd|reciprocal}}.
|Numerous {{cd|argument}} fields in density functions have been renamed.}}
|{{HistoryLine|||dev=snap6|Added the following density functions:
* {{cd|distance_to_point}}
* {{cd|log}}
* {{cd|pow}}
* {{cd|sign}}
* {{cd|slice}}
* {{cd|sqrt}}
|{{cd|end_islands}} has been renamed to {{cd|end_outer_islands}}.
|{{cd|y_clamped_gradient}} has been replaced with {{cd|gradient}}.
}}
|{{HistoryLine|||dev=snap7|Density functions are no longer evaluated with double-precision floating point values, but instead with single-precision.}}
|{{HistoryLine|||dev=snap10|Added the {{cd|ore_vein}} density function.
|{{cd|cache_once}} has been renamed to {{cd|cache}}.
|Added the {{cd|shift_x}}, {{cd|shift_y}}, and {{cd|shift_z}} fields to the {{cd|noise}} density function.
|Added the {{cd|cell_size_xz}} and {{cd|cell_size_y}} fields to the {{cd|interpolated}} density function.
|Removed the following density functions:
* {{cd|cache_2d}}
* {{cd|cache_all_in_cell}}
* {{cd|flat_cache}}
* {{cd|shifted_noise}}
}}
|{{HistoryLine|java upcoming}}
|{{HistoryLine|java upcoming}}
|{{HistoryLine||26.2|dev=snap5|Added density function {{cd|minecraft:interval_select}}.|Removed density function {{cd|minecraft:weird_scale_sampler}}. Its functionality has been replaced with {{cd|interval_select}}.}}
|{{HistoryLine||26.4|dev=snap5|{{cd|interpolated}} has been replaced with {{cd|upscale}}.}}
}}
}}


== Issues ==
== Issues ==
{{issue list|projects=MC}}
{{issue list|projects=MC}}
== References ==
{{reflist}}


== External links ==
== External links ==

Latest revision as of 11:16, 22 October 2026

Template:Exclusive Density functions make up mathematical expressions to obtain a number from a position, stored as Minecraft:JSON files within a Minecraft:data pack in the path data/<namespace>/worldgen/density_function. They are referenced from the Minecraft:noise router in Minecraft:noise settings.

Template:TOC

JSON format

A density function can be a constant number or an object.

If the Template:Nbt is constant, a shorthand format is:

  • Template:Nbt: A constant number. Value between −1000000.0 and 1000000.0 (both inclusive).

Marker functions

Template:Cd

If this density function is referenced twice, it is only computed once per block position.

Template:Cd

Template:Until

Interpolates at each block in one cell based on the input density function value of some cells around. The size of each cell is size_horizontal * 4 and size_vertical * 4.

Template:Cd

Samples the input function at a reduced resolution and upscales on each axis with the specified modes. Modes that require more samples will generally perform worse. Upscaling is peformed by axis in order of Z, X, then Y.Template:Upcoming

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, upscale).
    • Template:NbtTemplate:Nbt: Template:Json ref/density function — The input to sample.
    • Template:Nbt: Template:Cd; the configuration for this axis.
      • Template:Nbt: one of:
        • Template:Nbt: Value is discontinuous across cell boundaries, with the gradient always at 0. The values at cell vertices will always be equal to the cell value. One sample per axis.
        • Template:Nbt: Value is continuous, and the gradient is content with a cell but discontinuous across cell boundaries. The values at cell vertices will always be equal to the cell value. Two samples per axis.
        • Template:Nbt: Value and gradient are continuous, and the gradient is 0 at cell boundaries. The values at cell vertices will always be equal to the cell value. Two samples per axis.
        • Template:Nbt: Value and gradient are continuous. The values at cell vertices will always be equal to the cell value. Four samples per axis.
        • Template:Nbt: Value and gradient are continuous. The values at cell vertices do not necessarily need to equal to the cell value. Four samples per axis.
      • Template:Nbt: The size of each upscaling cell. Value between 1 and 64, inclusive.

Noise sampling functions

These density functions are used to sample noises.

Template:Cd

Samples a noise.

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, noise).
    • Template:Nbt: Template:Json ref — The noise to sample.
    • Template:Nbt: Scales the X and Z before sampling.
    • Template:Nbt: Scales the Y before sampling.
    • Template:Nbt: Optional; A domain warp to apply on X. If not specified, no warping will be applied (equivalent to 0).
    • Template:Nbt: Optional; A domain warp to apply on Y. If not specified, no warping will be applied (equivalent to 0).
    • Template:Nbt: Optional; A domain warp to apply on Z. If not specified, no warping will be applied (equivalent to 0).

Template:Cd

Samples a legacy noise. Template:Info needed

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, old_blended_noise).
    • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
    • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
    • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
    • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
    • Template:Nbt: Value between 1.0 and 8.0 (both inclusive).

Template:Cd

Samples a noise at (x/4, y/4, z/4), then multiplies it by 4.

Template:Cd

Samples a noise at (x/4, 0, z/4), then multiplies it by 4.

Template:Cd

Samples a noise at (z/4, x/4, 0), then multiplies it by 4.

Mathematical density functions

These density functions are used to perform mathematical operations.

Template:Cd

Calculates the absolute value of the input density function.

Template:Cd

Adds two density functions together.

Template:Cd

Rounds the input value to positive infinity.

Template:Cd

Clamps the input between two values.

Template:Cd

A constant value.

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, constant).
    • Template:Nbt: A constant value. Value between −1000000.0 and 1000000.0 (both inclusive).

Template:Cd

Cubes the input (x^3).

Template:Cd

Performs division between two arguments.

Template:Cd

Rounds the input value to negative infinity.

Template:Cd

Computes the natural logarithm of the given input.

Template:Cd

Multiplies two inputs.

Template:Cd

Returns the minimum of two inputs.

Template:Cd

Returns the maximum of two inputs.

Template:Cd

Negates the input.

Template:Cd

Raises the given base value to an exponent.

Template:Cd

Inverts the input (1/x).

Template:Cd

Rounds the input value to to the nearest integer (ties round up).

Template:Cd

Performs subtraction between two arguments.

Template:Cd

Computes the sign of the given input. If positive, it returns as 1. If the input is 0, it returns 0. If negative, it returns as -1.

Template:Cd

Computes the square root of the given input.

Template:Cd

Squares the input. (x^2)

Template:Cd

Rounds the input value to 0.

Mapped density functions

These density functions map a set of values onto another set of values.

Template:Cd

File:Gradient tiling.png
Demonstration of the different tiling options for the Template:Cd density function, using both an input range of -100 to 100 and an output range of -1 to 1.

Clamps the given coordinate and maps the gradient to a range.

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, gradient).
    • Template:Nbt: Template:Cd, Template:Cd. or Template:Cd: The axis over which to define the gradient .
    • Template:Nbt: How the density function handles values outside the specified coordinate range. 3 options:
      • clamp_to_edge: outside the gradient boundaries, the value at the nearest boundary will be used.
      • repeat: The gradient will be repeated outside its boundaries.
      • mirrored_repeat: The gradient will be repeated as such that odd repetitions are mirrored, ensuring continuity between repetitions.
    • Template:Nbt: The coordinate at which the gradient starts.
    • Template:Nbt: The coordinate at which the gradient ends. It must not equal Template:Cd.
    • Template:Nbt: The value at which the gradient starts.
    • Template:Nbt: The value at which the gradient ends.

Template:Cd

Performs (unclamped) linear interpolation between two arguments based on an alpha. The returned value is: first*(1-alpha) + second*alpha

Template:Cd

First clamps the input between −1 and 1, then transforms it using x/2 - x*x*x/24.

Template:Cd

Computes a cubic spline.

Conditional density functions

These density functions are used to apply "if-then" logic.

Template:Cd

If the input is negative, returns half of the input. Otherwise returns the input. (x < 0 ? x/2 : x)

Template:Cd

Selects between a number of density functions based on an input density function and a set of threshold values.

Template:Cd

If the input is negative, returns a quarter of the input. Otherwise returns the input. (x < 0 ? x/4 : x)

Template:Cd

Computes the input value, and depending on that result returns one of two other density functions. Basically an if-then-else statement.

Other density functions

Template:Cd

Adds beards for structures (see the terrain_adaptation field in structures). Its value is added to the final_density in noise setting by the game. Should not be referenced in data packs.

Template:Cd

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

Template:Cd

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

Template:Cd

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

Template:Cd

File:Distance to point options.png
Demonstration of the different metric options for the Template:Cd density function, using the distance from the point (0, 0).

Computes the distance to a fixed point using the specified distance function.

Template:Cd

Samples at current position using a noise algorithm used for end islands. Its minimum value is −0.84375 and its maximum value is 0.5625.

Template:Cd

Scans through a column of an input density and returns the topmost y-level that is above 0. If no such position exists within the bounds, the Template:Nbt is returned.

Template:Cd

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, ore_vein).
    • Template:Nbt: The ore block to place.
    • Template:Nbt: The raw ore block to place.
    • Template:Nbt: The filler block to place.
    • Template:Nbt: The probability for a raw ore block to be placed instead of an ore block. Value between 0 and 1 (inclusive).
    • Template:Nbt: The probability for the ore vein to replace a block. If the value is 0 or lower, no block will be replaced.
    • Template:Nbt: The probability for an ore block or a raw ore block to be placed, as opposed to Template:Cd. If the value is 0 or lower, all blocks will be the filler block. If the value is 1 or greater, no blocks will be the filler block.
    • Template:Nbt: Overrides Template:Cd; if the value is positive, Template:Cd will always be placed.

Template:Cd

Removes a dimension from the input domain by taking a "slice" along an axis with a specific coordinate (e.g. with the axis equaling y and the coordinate of 0, a slice will be taken along the XZ plane, with all values sampled at y=0).

Removed density functions

Template:Outdated

Template:Cd

Removed in Minecraft:26.3-snap10

Only computes the input density once per horizontal position.

Template:Cd

Removed in Minecraft:26.3-snap10

Used by the game onto final_density and should not be referenced in data packs.

Template:Cd

Removed in Minecraft:26.3-snap10

Calculate the value per 4×4 column (Value at each block in one column is the same). And it is calculated only once per column, at Y=0. Used often in combination with interpolated.

Template:Cd

Removed in Minecraft:26.3-snap10

Similar to noise, but first shifts the input coordinates.

Template:Cd

Removed in Minecraft:22w12a

The legacy "spline"

Removed in Minecraft:22w11a

Template:Cd

Removed in Minecraft:22w11a

Calculate the spline from the noise settings.

Template:Cd

Removed in Minecraft:26.2-snap5

According to the input value, scales and enhances (or weakens) some regions of the specified noise, and then returns the absolute value.

Template:Cd

Removed in Minecraft:26.3-snap6

Clamps the Y coordinate between from_y and to_y and then linearly maps it to a range.

  • Template:Nbt: Root object.
    • Template:Nbt: The ID of the density function type (in this case, y_clamped_gradient).
    • Template:Nbt: The value to be mapped to from_value. Value between −4064 and 4062 (both inclusive).
    • Template:Nbt: The value to be mapped to to_value. Value between −4064 and 4062 (both inclusive).
    • Template:Nbt: The value to map from_y to. Value between −1000000.0 and 1000000.0 (both inclusive).
    • Template:Nbt: The value to map to_y to. Value between −1000000.0 and 1000000.0 (both inclusive).

History

Template:HistoryTable

Issues

Template:Issue list

External links

Navigation

Template:Navbox Java Edition technical

Minecraft:de:Dichtefunktion Minecraft:fr:Fonction de densité Minecraft:ko:밀도 함수 Minecraft:pt:Função de densidade Minecraft:zh:密度函数

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