forked from mtcontrib/vector_extras
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Author | SHA1 | Date |
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bri cassa | 0501920345 | |
HybridDog | 63edf837d7 | |
bri cassa | 9bf8a890c6 | |
Desour | ed6b514057 | |
bri cassa | 374735b17f | |
HybridDog | f8c12047d5 | |
HybridDog | fdbcc2e425 | |
Sys Quatre | 2f0ad734d4 | |
Desour | 8c7aaf6c0b | |
Desour | e826bbd9b9 | |
Sys Quatre | a1f3da77c0 | |
HybridDog | 6f2bc919db | |
HybridDog | bc08421e20 | |
HybridDog | 8ddb3879fb | |
HybridDog | 275ec4af3b | |
HybridDog | f7dbb1a884 | |
HybridDog | d1a3c95286 | |
Sys Quatre | 6f5431097c | |
Sys Quatre | 268c6a0c36 | |
HybridDog | 9c6e53dd0a | |
HybridDog | dc368f7a7e |
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@ -0,0 +1,5 @@
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read_globals = {
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-- Defined by Minetest
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"minetest", "PseudoRandom", "VoxelArea", "string", "dump", "math"
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}
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globals = {"vector", "vector_extras_functions"}
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@ -1 +1 @@
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WTFPL
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CC0, except for code copied from e.g. minetest's builtin
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@ -1,2 +1,6 @@
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TODO:
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— maybe make the explosion table function return a perlin explosion table
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* maybe make the explosion table function return a perlin explosion table
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* Figure out and implement 3D scanline search
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* Add vector.hollowsphere, less positions than WorldEdit hollowsphere
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* Add unit tests
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* Use %a string format for vector.serialize so that it is reversible
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@ -0,0 +1,116 @@
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-- http://www.adammil.net/blog/v126_A_More_Efficient_Flood_Fill.html
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local can_go
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local marked_places
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local function calc_2d_index(x, y)
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return (y + 32768) * 65536 + x + 32768
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end
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local function mark(x, y)
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marked_places[calc_2d_index(x, y)] = true
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end
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local _fill
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local function fill(x, y)
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if can_go(x, y) then
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_fill(x, y)
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end
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end
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local corefill
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function _fill(x, y)
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while true do
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local ox = x
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local oy = y
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while can_go(x, y-1) do
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y = y-1
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end
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while can_go(x-1, y) do
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x = x-1
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end
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if x == ox
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and y == oy then
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break
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end
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end
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corefill(x, y)
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end
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function corefill(x, y)
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local lastcnt = 0
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repeat
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local cnt = 0
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local sx = x
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if lastcnt ~= 0
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and not can_go(y, x) then
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-- go right to find the x start
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repeat
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lastcnt = lastcnt-1
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if lastcnt == 0 then
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return
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end
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x = x+1
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until can_go(x, y)
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sx = x
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else
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-- go left if possible, and mark and _fill above
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while can_go(x-1, y) do
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x = x-1
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mark(x, y)
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if can_go(x, y-1) then
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_fill(x, y-1)
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end
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cnt = cnt+1
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lastcnt = lastcnt+1
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end
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end
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-- go right if possible, and mark
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while can_go(sx, y) do
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mark(sx, y)
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cnt = cnt+1
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sx = sx+1
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end
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if cnt < lastcnt then
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local e = x + lastcnt
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sx = sx+1
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while sx < e do
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if can_go(sx, y) then
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corefill(sx, y)
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end
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sx = sx+1
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end
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elseif cnt > lastcnt then
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local ux = x + lastcnt + 1
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while ux < sx do
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if can_go(ux, y-1) then
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_fill(ux, y-1)
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end
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ux = ux+1
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end
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end
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lastcnt = cnt
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y = y+1
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until lastcnt == 0
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end
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local function apply_fill(go_test, x0, y0, allow_revisit)
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if allow_revisit then
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can_go = go_test
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else
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local visited = {}
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can_go = function(x, y)
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local vi = calc_2d_index(x, y)
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if visited[vi] then
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return false
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end
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visited[vi] = true
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return go_test(x, y)
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end
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end
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marked_places = {}
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fill(x0, y0)
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return marked_places
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end
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return apply_fill
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@ -0,0 +1,154 @@
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# Vector helpers added by this mod
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## Helpers which return many positions for a shape, e.g. a line
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### Line functions
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These may be deprecated since raycasting has been added to minetest.
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See e.g. `minetest.line_of_sight`.
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* `vector.line([pos, dir[, range][, alt]])`: returns a table of vectors
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* `dir` is either a direction (when range is a number) or
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the start position (when range is the end position).
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* If alt is true, an old path calculation is used.
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* `vector.twoline(x, y)`: can return e.g. `{{0,0}, {0,1}}`
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* This is a lower-level function than `vector.line`; it can be used for
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a 2D line.
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* `vector.threeline(x, y, z)`: can return e.g. `{{0,0,0}, {0,1,0}}`
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* Similar to `vector.twoline`; this one is for the 3D case.
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* The parameters should be integers.
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* `vector.rayIter(pos, dir)`: returns an iterator for a for loop
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* `pos` can have non-integer values
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* `vector.fine_line([pos, dir[, range], scale])`: returns a table of vectors
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* Like `vector.line` but allows non-integer positions
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* It uses `vector.rayIter`.
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### Flood Fill
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* `vector.search_2d(go_test, x0, y0, allow_revisit, give_map)`: returns e.g.
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`{{0,0}, {0,1}}`
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* This function uses a Flood Fill algorithm, so it can be used to detect
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positions connected to each other in 2D.
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* `go_test(x, y)` should be a function which returns true iff the algorithm
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can "fill" at the position `(x, y)`.
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* `(x0, y0)` defines the start position.
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* If `allow_revisit` is false (the default), the function
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invokes `go_test` only once at every potential position.
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* If `give_map` is true (default is false), the function returns the
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marked table, whose indices are 2D vector indices, instead of a list of
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2D positions.
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* `vector.search_3d(can_go, startpos, apply_move, moves)`: returns FIXME
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* FIXME
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### Other Shapes
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* `vector.explosion_table(r)`: returns e.g. `{{pos1}, {pos2, true}}`
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* The returned list of positions and boolean represents a sphere;
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if the boolean is true, the position is on the outer side of the sphere.
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* It might be used for explosion calculations; but `vector.explosion_perlin`
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should make more realistic holes.
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* `vector.explosion_perlin(rmin, rmax[, nparams])`: returns e.g.
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`{{pos1}, {pos2, true}}`
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* This function is similar to `vector.explosion_table`; the positions
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do not represent a sphere but a more complex hole which is calculated
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with the help of perlin noise.
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* `rmin` and `rmax` represent the minimum and maximum radius,
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and `nparams` (which has a default value) are parameters for the perlin
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noise.
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* `vector.circle(r)`: returns a table of vectors
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* The returned positions represent a circle of radius `r` along the x and z
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directions; the y coordinates are all zero.
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* `vector.ring(r)`: returns a table of vectors
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* This function is similar to `vector.circle`; the positions are all
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touching each other (i.e. they are connected on whole surfaces and not
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only infinitely thin edges), so it is called `ring` instead of `circle`
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* `r` can be a non-integer number.
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* `vector.throw_parabola(pos, vel, gravity, point_count, time)`
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* FIXME: should return positions along a parabola so that moving objects
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collisions can be calculated
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* `vector.triangle(pos1, pos2, pos3)`: returns a table of positions, a number
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and a table with barycentric coordinates
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* This function calculates integer positions for a triangle defined by
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`pos1`, `pos2` and `pos3`, so it can be used to place polygons in
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minetest.
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* The returned number is the number of positions.
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* The barycentric coordinates are specified in a table with three elements;
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the first one corresponds to `pos1`, etc.
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## Helpers for various vector calculations
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* `vector.sort_positions(ps[, preferred_coords])`
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* Sorts a table of vectors `ps` along the coordinates specified in the
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table `preferred_coords` in-place.
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* If `preferred_coords` is omitted, it sorts along z, y and x in this order,
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where z has the highest priority.
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* `vector.maxnorm(v)`: returns the Tschebyshew norm of `v`
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* `vector.sumnorm(v)`: returns the Manhattan norm of `v`
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* `vector.pnorm(v, p)`: returns the `p` norm of `v`
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* `vector.inside(pos, minp, maxp)`: returns a boolean
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* Returns true iff `pos` is within the closed AABB defined by `minp`
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and `maxp`.
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* `vector.minmax(pos1, pos2)`: returns two vectors
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* This does the same as `worldedit.sort_pos`.
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* The components of the second returned vector are all bigger or equal to
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those of the first one.
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* `vector.move(pos1, pos2, length)`: returns a vector
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* Go from `pos1` `length` metres to `pos2` and then round to the nearest
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integer position.
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* Made for rubenwardy
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* `vector.from_number(i)`: returns `{x=i, y=i, z=i}`
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* `vector.chunkcorner(pos)`: returns a vector
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* Returns the mapblock position of the mapblock which contains
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the integer position `pos`
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* `vector.point_distance_minmax(p1, p2)`: returns two numbers
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* Returns the minimum and maximum of the absolute component-wise distances
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* `vector.collision(p1, p2)` FIXME
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* `vector.update_minp_maxp(minp, maxp, pos)`
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* Can change `minp` and `maxp` so that `pos` is within the AABB defined by
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`minp` and `maxp`
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* `vector.unpack(v)`: returns three numbers
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* Returns `v.z, v.y, v.x`
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* `vector.get_max_coord(v)`: returns a string
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* Returns `"x"`, `"y"` or `"z"`, depending on which component has the
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biggest value
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* `vector.get_max_coords(v)`: returns three strings
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* Similar to `vector.get_max_coord`; it returns the coordinates in the order
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of their component values
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* Example: `vector.get_max_coords{x=1, y=5, z=3}` returns `"y", "z", "x"`
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* `vector.serialize(v)`: returns a string
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* In comparison to `minetest.serialize`, this function uses a more compact
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string for the serialization.
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## Minetest-specific helper functions
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* `vector.straightdelay([length, vel[, acc]])`: returns a number
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* Returns the time an object takes to move `length` if it has velocity `vel`
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and acceleration `acc`
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* `vector.sun_dir([time])`: returns a vector or nil
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* Returns the vector which points to the sun
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* If `time` is omitted, it uses the current time.
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* This function does not yet support the moon;
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at night it simply returns `nil`.
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## Helpers which I don't recommend to use now
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* `vector.pos_to_string(pos)`: returns a string
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* It is similar to `minetest.pos_to_string`; it uses a different format:
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`"("..pos.x.."|"..pos.y.."|"..pos.z..")"`
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* `vector.zero`
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* The zero vector `{x=0, y=0, z=0}`
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* `vector.quickadd(pos, [z],[y],[x])`
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* Adds values to the vector components in-place
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## Deprecated helpers
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* `vector.plane`
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* should be removed soon; it should have done the same as vector.triangle
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|
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@ -0,0 +1,53 @@
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-- Algorithm created by sofar and changed by others:
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-- https://github.com/minetest/minetest/commit/d7908ee49480caaab63d05c8a53d93103579d7a9
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local function search(go, p, apply_move, moves)
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local num_moves = #moves
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-- We make a stack, and manually maintain size for performance.
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-- Stored in the stack, we will maintain tables with pos, and
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-- last neighbor visited. This way, when we get back to each
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-- node, we know which directions we have already walked, and
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-- which direction is the next to walk.
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local s = {}
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local n = 0
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-- The neighbor order we will visit from our table.
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local v = 1
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while true do
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-- Push current pos onto the stack.
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n = n + 1
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s[n] = {p = p, v = v}
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-- Select next node from neighbor list.
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p = apply_move(p, moves[v])
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-- Now we check out the node. If it is in need of an update,
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-- it will let us know in the return value (true = updated).
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if not go(p) then
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-- If we don't need to "recurse" (walk) to it then pop
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-- our previous pos off the stack and continue from there,
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-- with the v value we were at when we last were at that
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-- node
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repeat
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local pop = s[n]
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p = pop.p
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v = pop.v
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s[n] = nil
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n = n - 1
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-- If there's nothing left on the stack, and no
|
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-- more sides to walk to, we're done and can exit
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if n == 0 and v == num_moves then
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return
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end
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until v < num_moves
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-- The next round walk the next neighbor in list.
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v = v + 1
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else
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-- If we did need to walk the neighbor, then
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-- start walking it from the walk order start (1),
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-- and not the order we just pushed up the stack.
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v = 1
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||||
end
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end
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end
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|
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return search
|
339
init.lua
339
init.lua
|
@ -1,4 +1,4 @@
|
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local load_time_start = minetest.get_us_time()
|
||||
local path = minetest.get_modpath"vector_extras"
|
||||
|
||||
local funcs = {}
|
||||
|
||||
|
@ -6,7 +6,8 @@ function funcs.pos_to_string(pos)
|
|||
return "("..pos.x.."|"..pos.y.."|"..pos.z..")"
|
||||
end
|
||||
|
||||
local r_corr = 0.25 --remove a bit more nodes (if shooting diagonal) to let it look like a hole (sth like antialiasing)
|
||||
local r_corr = 0.25 --remove a bit more nodes (if shooting diagonal) to let it
|
||||
-- look like a hole (sth like antialiasing)
|
||||
|
||||
-- this doesn't need to be calculated every time
|
||||
local f_1 = 0.5-r_corr
|
||||
|
@ -51,6 +52,7 @@ local function return_line(pos, dir, range) --range ~= length
|
|||
local num = 1
|
||||
local t_dir = get_used_dir(dir)
|
||||
local dir_typ = t_dir[1]
|
||||
local f_tab
|
||||
if t_dir[3] == "+" then
|
||||
f_tab = {0, range, 1}
|
||||
else
|
||||
|
@ -121,7 +123,7 @@ function funcs.rayIter(pos, dir)
|
|||
for i in pairs(step) do
|
||||
choose[i] = vector.new(p)
|
||||
choose[i][i] = choose[i][i] + step[i]
|
||||
choosefit[i] = vector.scalar(vector.normalize(vector.subtract(choose[i], pos)), dir)
|
||||
choosefit[i] = vector.dot(vector.normalize(vector.subtract(choose[i], pos)), dir)
|
||||
end
|
||||
p = choose[vector.get_max_coord(choosefit)]
|
||||
|
||||
|
@ -255,18 +257,6 @@ function funcs.sort_positions(ps, preferred_coords)
|
|||
table.sort(ps, ps_sorting)
|
||||
end
|
||||
|
||||
function funcs.scalar(v1, v2)
|
||||
return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z
|
||||
end
|
||||
|
||||
function funcs.cross(v1, v2)
|
||||
return {
|
||||
x = v1.y*v2.z - v1.z*v2.y,
|
||||
y = v1.z*v2.x - v1.x*v2.z,
|
||||
z = v1.x*v2.y - v1.y*v2.x
|
||||
}
|
||||
end
|
||||
|
||||
-- Tschebyschew norm
|
||||
function funcs.maxnorm(v)
|
||||
return math.max(math.max(math.abs(v.x), math.abs(v.y)), math.abs(v.z))
|
||||
|
@ -284,7 +274,7 @@ end
|
|||
--local areas = {}
|
||||
function funcs.plane(ps)
|
||||
-- sort positions and imagine the first one (A) as vector.zero
|
||||
ps = vector.sort_positions(ps)
|
||||
vector.sort_positions(ps)
|
||||
local pos = ps[1]
|
||||
local B = vector.subtract(ps[2], pos)
|
||||
local C = vector.subtract(ps[3], pos)
|
||||
|
@ -303,29 +293,29 @@ function funcs.plane(ps)
|
|||
|
||||
local nAB = vector.normalize(B)
|
||||
local nAC = vector.normalize(C)
|
||||
local angle_BAC = math.acos(vector.scalar(nAB, nAC))
|
||||
local angle_BAC = math.acos(vector.dot(nAB, nAC))
|
||||
|
||||
local nBA = vector.multiply(nAB, -1)
|
||||
local nBC = vector.normalize(vector.subtract(C, B))
|
||||
local angle_ABC = math.acos(vector.scalar(nBA, nBC))
|
||||
local angle_ABC = math.acos(vector.dot(nBA, nBC))
|
||||
|
||||
for z = cube_p1.z, cube_p2.z do
|
||||
for y = cube_p1.y, cube_p2.y do
|
||||
for x = cube_p1.x, cube_p2.x do
|
||||
local p = {x=x, y=y, z=z}
|
||||
local n = -vector.scalar(p, vn)/vector.scalar(vn, vn)
|
||||
local n = -vector.dot(p, vn)/vector.dot(vn, vn)
|
||||
if math.abs(n) <= 0.5 then
|
||||
local ep = vector.add(p, vector.multiply(vn, n))
|
||||
local nep = vector.normalize(ep)
|
||||
local angle_BAep = math.acos(vector.scalar(nAB, nep))
|
||||
local angle_CAep = math.acos(vector.scalar(nAC, nep))
|
||||
local angle_BAep = math.acos(vector.dot(nAB, nep))
|
||||
local angle_CAep = math.acos(vector.dot(nAC, nep))
|
||||
local angldif = angle_BAC - (angle_BAep+angle_CAep)
|
||||
if math.abs(angldif) < 0.001 then
|
||||
ep = vector.subtract(ep, B)
|
||||
nep = vector.normalize(ep)
|
||||
local angle_ABep = math.acos(vector.scalar(nBA, nep))
|
||||
local angle_CBep = math.acos(vector.scalar(nBC, nep))
|
||||
local angldif = angle_ABC - (angle_ABep+angle_CBep)
|
||||
local angle_ABep = math.acos(vector.dot(nBA, nep))
|
||||
local angle_CBep = math.acos(vector.dot(nBC, nep))
|
||||
angldif = angle_ABC - (angle_ABep+angle_CBep)
|
||||
if math.abs(angldif) < 0.001 then
|
||||
table.insert(ps, vector.add(pos, p))
|
||||
end
|
||||
|
@ -344,7 +334,16 @@ function funcs.straightdelay(s, v, a)
|
|||
return (math.sqrt(v*v+2*a*s)-v)/a
|
||||
end
|
||||
|
||||
vector.zero = vector.new()
|
||||
-- override vector.zero
|
||||
-- builtin used not to have the vector.zero function. to keep compatibility,
|
||||
-- vector.zero has to be a 0-vector and vector.zero() has to return a 0-vector
|
||||
-- => we make a callable 0-vector table
|
||||
if not vector.zero then
|
||||
vector.zero = {x = 0, y = 0, z = 0}
|
||||
else
|
||||
local old_zero = vector.zero
|
||||
vector.zero = setmetatable({x = 0, y = 0, z = 0}, {__call = old_zero})
|
||||
end
|
||||
|
||||
function funcs.sun_dir(time)
|
||||
if not time then
|
||||
|
@ -369,9 +368,9 @@ function funcs.inside(pos, minp, maxp)
|
|||
return true
|
||||
end
|
||||
|
||||
function funcs.minmax(p1, p2)
|
||||
local p1 = vector.new(p1)
|
||||
local p2 = vector.new(p2)
|
||||
function funcs.minmax(pos1, pos2)
|
||||
local p1 = vector.new(pos1)
|
||||
local p2 = vector.new(pos2)
|
||||
for _,i in ipairs({"x", "y", "z"}) do
|
||||
if p1[i] > p2[i] then
|
||||
p1[i], p2[i] = p2[i], p1[i]
|
||||
|
@ -399,6 +398,66 @@ function funcs.from_number(i)
|
|||
return {x=i, y=i, z=i}
|
||||
end
|
||||
|
||||
local adammil_fill = dofile(path .. "/adammil_flood_fill.lua")
|
||||
function funcs.search_2d(go_test, x0, y0, allow_revisit, give_map)
|
||||
local marked_places = adammil_fill(go_test, x0, y0, allow_revisit)
|
||||
if give_map then
|
||||
return marked_places
|
||||
end
|
||||
local l = {}
|
||||
for vi in pairs(marked_places) do
|
||||
local x = (vi % 65536) - 32768
|
||||
local y = (math.floor(x / 65536) % 65536) - 32768
|
||||
l[#l+1] = {x, y}
|
||||
end
|
||||
return l
|
||||
end
|
||||
|
||||
local fallings_search = dofile(path .. "/fill_3d.lua")
|
||||
local moves_touch = {
|
||||
{x = -1, y = 0, z = 0},
|
||||
{x = 0, y = 0, z = 0}, -- FIXME should this be here?
|
||||
{x = 1, y = 0, z = 0},
|
||||
{x = 0, y = -1, z = 0},
|
||||
{x = 0, y = 1, z = 0},
|
||||
{x = 0, y = 0, z = -1},
|
||||
{x = 0, y = 0, z = 1},
|
||||
}
|
||||
local moves_near = {}
|
||||
for z = -1,1 do
|
||||
for y = -1,1 do
|
||||
for x = -1,1 do
|
||||
moves_near[#moves_near+1] = {x = x, y = y, z = z}
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function funcs.search_3d(can_go, startpos, apply_move, moves)
|
||||
local visited = {}
|
||||
local found = {}
|
||||
local function on_visit(pos)
|
||||
local vi = minetest.hash_node_position(pos)
|
||||
if visited[vi] then
|
||||
return false
|
||||
end
|
||||
visited[vi] = true
|
||||
local valid_pos = can_go(pos)
|
||||
if valid_pos then
|
||||
found[#found+1] = pos
|
||||
end
|
||||
return valid_pos
|
||||
end
|
||||
if apply_move == "touch" then
|
||||
apply_move = vector.add
|
||||
moves = moves_touch
|
||||
elseif apply_move == "near" then
|
||||
apply_move = vector.add
|
||||
moves = moves_near
|
||||
end
|
||||
fallings_search(on_visit, startpos, apply_move, moves)
|
||||
end
|
||||
|
||||
|
||||
local explosion_tables = {}
|
||||
function funcs.explosion_table(r)
|
||||
local table = explosion_tables[r]
|
||||
|
@ -449,7 +508,8 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
|
|||
nparams.spread = nparams.spread or vector.from_number(r*5)
|
||||
|
||||
local pos = {x=math.random(-30000, 30000), y=math.random(-30000, 30000), z=math.random(-30000, 30000)}
|
||||
local map = minetest.get_perlin_map(nparams, vector.from_number(r+r+1)):get3dMap_flat(pos)
|
||||
local map = minetest.get_perlin_map(nparams, vector.from_number(r+r+1)
|
||||
):get3dMap_flat(pos)
|
||||
|
||||
local id = 1
|
||||
|
||||
|
@ -464,11 +524,11 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
|
|||
|
||||
local tab, n = {}, 1
|
||||
for z=-r,r do
|
||||
local bare_dist = z*z
|
||||
local bare_dist_z = z*z
|
||||
for y=-r,r do
|
||||
local bare_dist = bare_dist+y*y
|
||||
local bare_dist_yz = bare_dist_z + y*y
|
||||
for x=-r,r do
|
||||
local bare_dist = bare_dist+x*x
|
||||
local bare_dist = bare_dist_yz + x*x
|
||||
local add = bare_dist < bare_mindist
|
||||
local pval, distdiv
|
||||
if not add
|
||||
|
@ -494,22 +554,19 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
|
|||
end
|
||||
end
|
||||
|
||||
map = nil
|
||||
collectgarbage()
|
||||
|
||||
-- change strange values
|
||||
local pval_diff = pval_max - pval_min
|
||||
pval_min = pval_min/pval_diff
|
||||
|
||||
for n,i in pairs(tab) do
|
||||
for k,i in pairs(tab) do
|
||||
if i[2] then
|
||||
local new_pval = math.abs(i[2]/pval_diff - pval_min)
|
||||
if i[3]+0.33 < new_pval then
|
||||
tab[n] = {i[1]}
|
||||
tab[k] = {i[1]}
|
||||
elseif i[3] < new_pval then
|
||||
tab[n] = {i[1], true}
|
||||
tab[k] = {i[1], true}
|
||||
else
|
||||
tab[n] = nil
|
||||
tab[k] = nil
|
||||
end
|
||||
end
|
||||
end
|
||||
|
@ -584,67 +641,6 @@ function funcs.ring(r)
|
|||
return tab2
|
||||
end
|
||||
|
||||
--~ posy(t) = att + bt + c
|
||||
--~ vely(t) = 2at + b
|
||||
--~ accy(t) = 2a
|
||||
|
||||
--~ a = -0.5gravity
|
||||
--~ vely(0) = b = vel.y
|
||||
--~ posy(0) = c = pos.y
|
||||
|
||||
--~ posy(t) = -0.5 * gravity * t * t + vel.y * t + pos.y
|
||||
--~ vely(t) = -gravity*t + vel.y
|
||||
|
||||
--~ Scheitel:
|
||||
--~ vely(t) = 0 = -gravity*t + vel.y
|
||||
--~ t = vel.y / gravity
|
||||
|
||||
--~ 45°
|
||||
--~ vely(t)^2 = velx(t)^2 + velz(t)^2
|
||||
--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
|
||||
--~ gravity^2 * t^2 + vel.y^2 - -2*gravity*t*vel.y = vel.x * vel.x + vel.z * vel.z
|
||||
--~ gravity^2 * t^2 - 2*gravity*vel.y * t + (vel.y^2 - vel.x^2 - vel.z^2) = 0
|
||||
--~ t = (2*gravity*vel.y .. rt((2*gravity*vel.y)^2 - 4*gravity^2*(vel.y^2 - vel.x^2 - vel.z^2))) / (2*gravity^2)
|
||||
--~ t = (2*gravity*vel.y .. rt(4*gravity^2*vel.y^2 - 4*gravity^2*(vel.y^2) + 4*gravity^2*(vel.x^2 + vel.z^2))) / (2*gravity^2)
|
||||
--~ t = (2*gravity*vel.y .. 2*gravity*rt(vel.x^2 + vel.z^2)) / (2*gravity^2)
|
||||
--~ t = (vel.y .. rt(vel.x^2 + vel.z^2)) / gravity
|
||||
--~ t1 = (vel.y - math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
|
||||
--~ t2 = (vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
|
||||
|
||||
--~ yswitch = posy(t1) (= posy(t2)) //links und rechts gleich
|
||||
--~ yswitch = -0.5 * gravity * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity)^2 + vel.y * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
|
||||
--~ yswitch = -0.5 * gravity * (vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z))^2 / gravity^2 + vel.y * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
|
||||
--~ yswitch = -0.5 * (vel.y^2 + 2*vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.x^2 + vel.z^2) / gravity + ((vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
|
||||
--~ yswitch = (-0.5 * (vel.y^2 + 2*vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.x^2 + vel.z^2) + ((vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)))) / gravity + pos.y
|
||||
--~ yswitch = (-0.5 * vel.y^2 - vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) - 0.5 * vel.x^2 - 0.5 * vel.z^2 + vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity + pos.y
|
||||
--~ yswitch = (-0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2 + vel.y^2) / gravity + pos.y
|
||||
--~ yswitch = (0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2) / gravity + pos.y
|
||||
--~ yswitch = -0.5 * (vel.x * vel.x + vel.z * vel.z - vel.y * vel.y) / gravity + pos.y
|
||||
|
||||
|
||||
--~ 45° Zeitpunkte kleineres beim Aufstieg, größeres beim Fall
|
||||
--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
|
||||
--~ -gravity*t + vel.y = ..math.sqrt(vel.x * vel.x + vel.z * vel.z)
|
||||
--~ t = (..math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
|
||||
--~ t_raise = (-math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
|
||||
--~ t_fall = (math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
|
||||
|
||||
--~ posy nach t umstellen
|
||||
--~ y = -0.5 * gravity * t * t + vel.y * t + pos.y
|
||||
--~ 0 = -0.5 * gravity * t * t + vel.y * t + pos.y - y
|
||||
--~ t = (-vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / (-gravity)
|
||||
--~ t = (vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
|
||||
--~ t_up = (vel.y - math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
|
||||
--~ t_down = (vel.y + math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
|
||||
|
||||
--~ posx(t) = vel.x * t + pos.x
|
||||
--~ posz(t) = vel.z * t + pos.z
|
||||
|
||||
--~ posx nach t umstellen
|
||||
--~ posx - pos.x = vel.x * t
|
||||
--~ t = (posx - pos.x) / vel.x
|
||||
|
||||
|
||||
local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount,
|
||||
time)
|
||||
local pointcount = 0
|
||||
|
@ -654,9 +650,9 @@ local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount,
|
|||
/ gravity + pos.y
|
||||
|
||||
-- the times of the 45° angle point
|
||||
local i = math.sqrt(vel.x^2 + vel.z^2)
|
||||
local t_raise_end = (-i + vel.y) / gravity
|
||||
local t_fall_start = (i + vel.y) / gravity
|
||||
local vel_len = math.sqrt(vel.x^2 + vel.z^2)
|
||||
local t_raise_end = (-vel_len + vel.y) / gravity
|
||||
local t_fall_start = (vel_len + vel.y) / gravity
|
||||
if t_fall_start > 0 then
|
||||
-- the right 45° angle point wasn't passed yet
|
||||
if t_raise_end > 0 then
|
||||
|
@ -785,11 +781,11 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
|
|||
-- get a list of possible positions between
|
||||
local diff = vector.subtract(p2, p)
|
||||
local possible_positions = {}
|
||||
for i,v in pairs(diff) do
|
||||
for c,v in pairs(diff) do
|
||||
if v ~= 0 then
|
||||
local p = vector.new(p)
|
||||
p[i] = p[i] + v
|
||||
possible_positions[#possible_positions+1] = p
|
||||
local pos_moved = vector.new(p)
|
||||
pos_moved[c] = pos_moved[c] + v
|
||||
possible_positions[#possible_positions+1] = pos_moved
|
||||
end
|
||||
end
|
||||
-- test which one fits best
|
||||
|
@ -800,12 +796,12 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
|
|||
z = vel.z * t + pos.z,
|
||||
}
|
||||
local d = math.huge
|
||||
for i = 1,2 do
|
||||
local pos = possible_positions[i]
|
||||
local dist = vector.distance(pos, near_p)
|
||||
if dist < d then
|
||||
p = pos
|
||||
d = dist
|
||||
for k = 1,2 do
|
||||
local pos_moved = possible_positions[k]
|
||||
local dist_current = vector.distance(pos_moved, near_p)
|
||||
if dist_current < d then
|
||||
p = pos_moved
|
||||
d = dist_current
|
||||
end
|
||||
end
|
||||
-- add it
|
||||
|
@ -816,11 +812,11 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
|
|||
-- get a list of possible positions between
|
||||
local diff = vector.subtract(p2, p)
|
||||
local possible_positions = {}
|
||||
for i,v in pairs(diff) do
|
||||
for c,v in pairs(diff) do
|
||||
if v ~= 0 then
|
||||
local p = vector.new(p)
|
||||
p[i] = p[i] + v
|
||||
possible_positions[#possible_positions+1] = p
|
||||
local pos_moved = vector.new(p)
|
||||
pos_moved[c] = pos_moved[c] + v
|
||||
possible_positions[#possible_positions+1] = pos_moved
|
||||
end
|
||||
end
|
||||
-- test which one fits best
|
||||
|
@ -832,12 +828,12 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
|
|||
}
|
||||
local d = math.huge
|
||||
assert(#possible_positions == 4-k, "how, number positions?")
|
||||
for i = 1,4-k do
|
||||
local pos = possible_positions[i]
|
||||
local dist = vector.distance(pos, near_p)
|
||||
if dist < d then
|
||||
p = pos
|
||||
d = dist
|
||||
for j = 1,4-k do
|
||||
local pos_moved = possible_positions[j]
|
||||
local dist_current = vector.distance(pos_moved, near_p)
|
||||
if dist_current < d then
|
||||
p = pos_moved
|
||||
d = dist_current
|
||||
end
|
||||
end
|
||||
-- add it
|
||||
|
@ -858,9 +854,9 @@ function funcs.chunkcorner(pos)
|
|||
return {x=pos.x-pos.x%16, y=pos.y-pos.y%16, z=pos.z-pos.z%16}
|
||||
end
|
||||
|
||||
function funcs.point_distance_minmax(p1, p2)
|
||||
local p1 = vector.new(p1)
|
||||
local p2 = vector.new(p2)
|
||||
function funcs.point_distance_minmax(pos1, pos2)
|
||||
local p1 = vector.new(pos1)
|
||||
local p2 = vector.new(pos2)
|
||||
local min, max, vmin, vmax, num
|
||||
for _,i in ipairs({"x", "y", "z"}) do
|
||||
num = math.abs(p1[i] - p2[i])
|
||||
|
@ -877,21 +873,20 @@ function funcs.point_distance_minmax(p1, p2)
|
|||
end
|
||||
|
||||
function funcs.collision(p1, p2)
|
||||
local clear, node_pos, collision_pos, max, dmax, dcmax, pt
|
||||
clear, node_pos = minetest.line_of_sight(p1, p2)
|
||||
local clear, node_pos = minetest.line_of_sight(p1, p2)
|
||||
if clear then
|
||||
return false
|
||||
end
|
||||
collision_pos = {}
|
||||
min, max = funcs.point_distance_minmax(node_pos, p2)
|
||||
local collision_pos = {}
|
||||
local _, max = funcs.point_distance_minmax(node_pos, p2)
|
||||
if node_pos[max] > p2[max] then
|
||||
collision_pos[max] = node_pos[max] - 0.5
|
||||
else
|
||||
collision_pos[max] = node_pos[max] + 0.5
|
||||
end
|
||||
dmax = p2[max] - node_pos[max]
|
||||
dcmax = p2[max] - collision_pos[max]
|
||||
pt = dcmax/dmax
|
||||
local dmax = p2[max] - node_pos[max]
|
||||
local dcmax = p2[max] - collision_pos[max]
|
||||
local pt = dcmax / dmax
|
||||
|
||||
for _,i in ipairs({"x", "y", "z"}) do
|
||||
collision_pos[i] = p2[i] - (p2[i] - node_pos[i]) * pt
|
||||
|
@ -958,10 +953,77 @@ function funcs.serialize(vec)
|
|||
return "{x=" .. vec.x .. ",y=" .. vec.y .. ",z=" .. vec.z .. "}"
|
||||
end
|
||||
|
||||
function funcs.triangle(pos1, pos2, pos3)
|
||||
local normal = vector.cross(vector.subtract(pos2, pos1),
|
||||
vector.subtract(pos3, pos1))
|
||||
-- Find the biggest absolute component of the normal vector
|
||||
local dir = vector.get_max_coord({
|
||||
x = math.abs(normal.x),
|
||||
y = math.abs(normal.y),
|
||||
z = math.abs(normal.z),
|
||||
})
|
||||
-- Find the other directions for the for loops
|
||||
local all_other_dirs = {
|
||||
x = {"z", "y"},
|
||||
y = {"z", "x"},
|
||||
z = {"y", "x"},
|
||||
}
|
||||
local other_dirs = all_other_dirs[dir]
|
||||
local odir1, odir2 = other_dirs[1], other_dirs[2]
|
||||
|
||||
local pos1_2d = {pos1[odir1], pos1[odir2]}
|
||||
local pos2_2d = {pos2[odir1], pos2[odir2]}
|
||||
local pos3_2d = {pos3[odir1], pos3[odir2]}
|
||||
-- The boundaries of the 2D AABB along other_dirs
|
||||
local p1 = {}
|
||||
local p2 = {}
|
||||
for i = 1,2 do
|
||||
p1[i] = math.floor(math.min(pos1_2d[i], pos2_2d[i], pos3_2d[i]))
|
||||
p2[i] = math.ceil(math.max(pos1_2d[i], pos2_2d[i], pos3_2d[i]))
|
||||
end
|
||||
|
||||
-- https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/rasterization-stage
|
||||
local function edgefunc(vert1, vert2, pos)
|
||||
return (pos[1] - vert1[1]) * (vert2[2] - vert1[2])
|
||||
- (pos[2] - vert1[2]) * (vert2[1] - vert1[1])
|
||||
end
|
||||
-- eps is used to prevend holes in neighbouring triangles
|
||||
-- It should be smaller than the smallest possible barycentric value
|
||||
-- FIXME: I'm not sure if it really does what it should.
|
||||
local eps = 0.5 / math.max(p2[1] - p1[1], p2[2] - p1[2])
|
||||
local a_all_inv = 1.0 / edgefunc(pos1_2d, pos2_2d, pos3_2d)
|
||||
local step_k3 = - (pos2_2d[1] - pos1_2d[1]) * a_all_inv
|
||||
local step_k1 = - (pos3_2d[1] - pos2_2d[1]) * a_all_inv
|
||||
-- Calculate the triangle points
|
||||
local points = {}
|
||||
local barycentric_coords = {}
|
||||
local n = 0
|
||||
-- It is possible to further optimize this
|
||||
for v1 = p1[1], p2[1] do
|
||||
local p = {v1, p1[2]}
|
||||
local k3 = edgefunc(pos1_2d, pos2_2d, p) * a_all_inv
|
||||
local k1 = edgefunc(pos2_2d, pos3_2d, p) * a_all_inv
|
||||
for _ = p1[2], p2[2] do
|
||||
local k2 = 1 - k1 - k3
|
||||
if k1 >= -eps and k2 >= -eps and k3 >= -eps then
|
||||
-- On triangle
|
||||
local h = math.floor(k1 * pos1[dir] + k2 * pos2[dir] +
|
||||
k3 * pos3[dir] + 0.5)
|
||||
n = n+1
|
||||
points[n] = {[odir1] = v1, [odir2] = p[2], [dir] = h}
|
||||
barycentric_coords[n] = {k1, k2, k3}
|
||||
end
|
||||
p[2] = p[2]+1
|
||||
k3 = k3 + step_k3
|
||||
k1 = k1 + step_k1
|
||||
end
|
||||
end
|
||||
return points, n, barycentric_coords
|
||||
end
|
||||
|
||||
|
||||
vector_extras_functions = funcs
|
||||
|
||||
local path = minetest.get_modpath"vector_extras"
|
||||
dofile(path .. "/legacy.lua")
|
||||
--dofile(minetest.get_modpath("vector_extras").."/vector_meta.lua")
|
||||
|
||||
|
@ -977,11 +1039,4 @@ for name,func in pairs(funcs) do
|
|||
end
|
||||
end
|
||||
|
||||
|
||||
local time = (minetest.get_us_time() - load_time_start) / 1000000
|
||||
local msg = "[vector_extras] loaded after ca. " .. time .. " seconds."
|
||||
if time > 0.01 then
|
||||
print(msg)
|
||||
else
|
||||
minetest.log("action", msg)
|
||||
end
|
||||
minetest.log("action", "[vector_extras] loaded.")
|
||||
|
|
|
@ -1,5 +1,11 @@
|
|||
local funcs = vector_extras_functions
|
||||
|
||||
function funcs.scalar(v1, v2)
|
||||
minetest.log("deprecated", "[vector_extras] vector.scalar is " ..
|
||||
"deprecated, use vector.dot instead.")
|
||||
return vector.dot(v1, v2)
|
||||
end
|
||||
|
||||
function funcs.get_data_from_pos(tab, z,y,x)
|
||||
minetest.log("deprecated", "[vector_extras] get_data_from_pos is " ..
|
||||
"deprecated, use the minetest pos hash function instead.")
|
||||
|
|
|
@ -94,15 +94,15 @@ function vector.meta.complete_node_table(pos, name) --neccesary because tab[1] w
|
|||
if not tmp then
|
||||
vector.meta.nodes[pos.x] = {}
|
||||
end
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y]
|
||||
if not tmp then
|
||||
vector.meta.nodes[pos.x][pos.y] = {}
|
||||
end
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
|
||||
if not tmp then
|
||||
vector.meta.nodes[pos.x][pos.y][pos.z] = {}
|
||||
end
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
|
||||
if not tmp then
|
||||
vector.meta.nodes[pos.x][pos.y][pos.z][name] = {}
|
||||
end
|
||||
|
@ -117,12 +117,12 @@ function vector.meta.get_node(pos, name)
|
|||
or table_empty(tmp) then
|
||||
return false
|
||||
end
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y]
|
||||
if not tmp
|
||||
or table_empty(tmp) then
|
||||
return false
|
||||
end
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
|
||||
if not tmp
|
||||
or table_empty(tmp) then
|
||||
return false
|
||||
|
@ -133,7 +133,7 @@ function vector.meta.get_node(pos, name)
|
|||
return true
|
||||
end
|
||||
|
||||
local tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
|
||||
tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
|
||||
if not tmp
|
||||
or table_empty(tmp) then
|
||||
return false
|
||||
|
|
Loading…
Reference in New Issue