Mount Gen: add parabola algorithm. Closes #1931

mods/lord/World/mountgen/src/mountgen.lua

@@ -1,5 +1,6 @@
 local Algorithm              = require('mountgen.Algorithm')
 local ConeAlgorithm          = require('mountgen.algorithm.Cone')
+local ParabolaAlgorithm      = require('mountgen.algorithm.Parabola')
 local DiamondSquareAlgorithm = require('mountgen.algorithm.DiamondSquare')
 local Form                   = require('mountgen.config.Form')
 local Generator              = require('mountgen.Generator')
@@ -24,6 +25,7 @@ end
 local function register_algorithms()
 	Algorithm
 		.register(ConeAlgorithm)
+		.register(ParabolaAlgorithm)
 		.register(DiamondSquareAlgorithm)
 end
 

mods/lord/World/mountgen/src/mountgen/algorithm/Cone.lua

@@ -68,7 +68,7 @@ end
 
 --- Generate mountain as cone
 --- @param top_pos Position
---- @param config  mountgen.ConfigValues
+--- @param config  mountgen.algorithm.Cone.ConfigValues
 --- @return mountgen.generator.HeightMap, number, number "height map, map size, center_coordinate"
 function Cone.build_height_map(top_pos, config)
 	local H = top_pos.y - config.foot_height               -- height of truncated cone

mods/lord/World/mountgen/src/mountgen/algorithm/DiamondSquare.lua

@@ -139,7 +139,7 @@ end
 
 --- Generate mountain with diamond-square algorithm
 --- @param top    Position
---- @param config mountgen.ConfigValues
+--- @param config mountgen.algorithm.DiamondSquare.ConfigValues
 --- @return mountgen.generator.HeightMap, number, number "height map, map size, center coordinate"
 function DiamondSquare.build_height_map(top, config)
 	local H = top.y - config.foot_height

mods/lord/World/mountgen/src/mountgen/algorithm/Parabola.lua

@@ -0,0 +1,126 @@
+local math_min, math_limit, math_abs, math_floor, math_ceil, math_sqrt
+    = math.min, math.limit, math.abs, math.floor, math.ceil, math.sqrt
+
+local HeightMap = require('mountgen.generator.HeightMap')
+local FieldType = require('mountgen.config.FieldType')
+
+local S = minetest.get_mod_translator()
+
+
+--- @class mountgen.algorithm.Parabola.ConfigValues: mountgen.config.ValuesTable
+--- @field multiplier number coefficient `k` in formula `y = - k * x^2 + b`
+--- @field shift_up   number coefficient `b` in formula `y = - k * x^2 + b`
+--- @field max_radius number maximum radius of generated mountain
+
+--- @alias mountgen.ParabolaCfgValues mountgen.algorithm.Parabola.ConfigValues
+
+--- @class mountgen.algorithm.Parabola: mountgen.AlgorithmInterface
+local Parabola = {
+	--- @public
+	--- @const
+	--- @type string
+	NAME = 'parabola',
+	--- @private
+	--- @const
+	--- @type mountgen.config.FieldDefinition[]
+	CONFIG_FIELDS = {
+		multiplier = {
+			name        = 'multiplier',
+			type        = FieldType.NUMBER,
+			label       = S('Multiplier coefficient (k)'),
+			description =
+				S('This makes vertical stretching/compression of mountain.') .. '\n' ..
+				S('Coefficient `k` in formula `y = - k * x^2 + b`')
+			,
+		},
+		shift_up = {
+			name        = 'shift_up',
+			type        = FieldType.NUMBER,
+			label       = S('Shift up (b)'),
+			description =
+				S('How much the generated mountain will be shifted up.') .. '\n' ..
+				S('The mountain will be cut off at the player\'s position;') .. ' ' ..
+				S('and no mountain will be generated above the player.') .. '\n' ..
+				S('Parameter `b` in formula `y = - k * x^2 + b`')
+			,
+		},
+		max_radius = {
+			name        = 'max_radius',
+			type        = FieldType.NUMBER,
+			label       = S('Max radius'),
+			description = S('Maximum radius of generated cone.'),
+		}
+	},
+	--- @private
+	--- @const
+	--- @type table
+	CONFIG_DEFAULTS = {
+		--- @type number
+		multiplier = 0.02,
+		--- @type number
+		shift_up   = 1,
+		--- @type number
+		max_radius = 20,
+	}
+}
+
+--- @return string
+function Parabola.get_description()
+	return
+		S('The `Parabola` algorithm builds a part of the mountain in the form of inverted (upside down) parabola.') .. '\n' ..
+		S('It is well suited on a small scale for more detailed landscape construction.') .. '\n' ..
+		S('Used formula: `y = -k * x^2 + b + mountain_height`.')
+end
+
+--- @return mountgen.config.FieldDefinition[]
+function Parabola.get_config_fields()
+	return Parabola.CONFIG_FIELDS
+end
+
+--- @return table
+function Parabola.get_config_defaults()
+	return Parabola.CONFIG_DEFAULTS
+end
+
+--- Generate mountain as cone
+--- @param top_pos Position
+--- @param config  mountgen.algorithm.Parabola.ConfigValues
+--- @return mountgen.generator.HeightMap, number, number "height map, map size, center_coordinate"
+function Parabola.build_height_map(top_pos, config)
+	-- Used formula: `y = -k * x^2 + b + mountain_height`
+	local n = 2                 -- pow
+	local k = config.multiplier
+	local b = config.shift_up
+
+	-- Inverse formula: x = sqrt{n}((y - b - mountain_top) / -k)
+	-- Inverse formula: x = ((y - b - mountain_top) / -k) ^ (1/2)
+	local H = top_pos.y - config.foot_height
+	-- Lets `x = 0`, so we can to calc width of mountain at the foot
+	local W = math_ceil(2 * math_abs(((0 - b - H) / -k) ^ (1/n)))
+
+	local height   = H
+
+	local height_map_size   = math_min(W, 2 * config.max_radius)
+	local height_map_radius = math_floor(height_map_size / 2)
+	local height_map        = HeightMap:new(height_map_size)
+
+	for z = 0, height_map_size - 1 do
+		for x = 0, height_map_size - 1 do
+			local px = x - height_map_radius
+			local pz = z - height_map_radius
+
+			local dfc = math_sqrt(px^2 + pz^2) -- distance from the center
+
+			if dfc <= height_map_radius then
+				-- Used formula: `y = -k * x^2 + b + mountain_height`
+				local h = - k * dfc^n + b + height
+				height_map:set_value(z, x, math_limit(h, 0, H))
+			end
+		end
+	end
+
+	return height_map, height_map_size, height_map_radius
+end
+
+
+return Parabola