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Fix parabola calculation mistakes, parabola works
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Hybrid Dog
parent
2fce6dbdc9
commit
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103
init.lua
103
init.lua
@ -577,7 +577,7 @@ end
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--~ vely(0) = b = vel.y
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--~ posy(0) = c = pos.y
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--~ posy(t) = -0.5gravity*tt + vel.y*t + pos.y
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--~ posy(t) = -0.5 * gravity * t * t + vel.y * t + pos.y
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--~ vely(t) = -gravity*t + vel.y
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--~ Scheitel:
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@ -585,31 +585,42 @@ end
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--~ t = vel.y / gravity
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--~ 45°
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--~ vely(t) = +/-1 = -gravity*t + vel.y
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--~ t = (vel.y - 1) / gravity //links
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--~ t = (vel.y + 1) / gravity //rechts
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--~ vely(t)^2 = velx(t)^2 + velz(t)^2
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--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
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--~ gravity^2 * t^2 + vel.y^2 - -2*gravity*t*vel.y = vel.x * vel.x + vel.z * vel.z
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--~ gravity^2 * t^2 - 2*gravity*vel.y * t + (vel.y^2 - vel.x^2 - vel.z^2) = 0
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--~ 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)
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--~ 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)
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--~ t = (2*gravity*vel.y .. 2*gravity*rt(vel.x^2 + vel.z^2)) / (2*gravity^2)
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--~ t = (vel.y .. rt(vel.x^2 + vel.z^2)) / gravity
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--~ t1 = (vel.y - math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
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--~ t2 = (vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
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--~ yswitch = posy(t) //links und rechts gleich
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--~ yswitch = -0.5gravity*((vel.y + 1) / gravity)^2 + vel.y*(vel.y + 1) / gravity + pos.y
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--~ yswitch = -0.5(vel.y + 1)^2 / gravity + (vel.y^2 + vel.y) / gravity + pos.y
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--~ yswitch = -0.5(vel.y^2 + 2vel.y + 1) / gravity + (vel.y^2 + vel.y) / gravity + pos.y
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--~ yswitch = (-0.5vel.y^2 - vel.y - 0.5 + vel.y^2 + vel.y) / gravity + pos.y
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--~ yswitch = (0.5vel.y^2 - 0.5) / gravity + pos.y
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--~ yswitch = posy(t1) (= posy(t2)) //links und rechts gleich
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--~ 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
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--~ 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
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--~ 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
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--~ 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
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--~ 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
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--~ yswitch = (-0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2 + vel.y^2) / gravity + pos.y
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--~ yswitch = (0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2) / gravity + pos.y
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--~ yswitch = -0.5 * (vel.x * vel.x + vel.z * vel.z - vel.y * vel.y) / gravity + pos.y
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--~ yswitch = -0.5gravity*((vel.y - 1) / gravity)^2 + vel.y*(vel.y - 1) / gravity + pos.y
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--~ yswitch = -0.5(vel.y - 1)^2 / gravity + (vel.y^2 - vel.y) / gravity + pos.y
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--~ yswitch = (-0.5(vel.y - 1)^2 + vel.y^2 - vel.y) / gravity + pos.y
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--~ yswitch = (-0.5(vel.y^2 - 2vel.y + 1) + vel.y^2 - vel.y) / gravity + pos.y
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--~ yswitch = (-0.5vel.y^2 + vel.y - 0.5 + vel.y^2 - vel.y) / gravity + pos.y
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--~ yswitch = (0.5vel.y^2 - 0.5) / gravity + pos.y
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--~ posy nach t umstellen, kleineres beim Aufstieg, größeres beim Fall
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--~ posy = -0.5gravity*tt + vel.y*t + pos.y
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--~ 0 = -0.5gravity*tt + vel.y*t + pos.y - posy //→Mitternachtsformel
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--~ t = -vel.y +-rt(vel.y^2 -4(-0.5gravity)(pos.y - posy)) / 2(-0.5gravity)
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--~ t = -vel.y +-rt(vel.y^2 +2gravity(pos.y - posy)) / gravity
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--~ t_rise = -vel.y - rt(vel.y^2 +2gravity(pos.y - posy)) / gravity
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--~ t_fall = -vel.y + rt(vel.y^2 +2gravity(pos.y - posy)) / gravity
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--~ 45° Zeitpunkte kleineres beim Aufstieg, größeres beim Fall
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--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
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--~ -gravity*t + vel.y = ..math.sqrt(vel.x * vel.x + vel.z * vel.z)
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--~ t = (..math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
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--~ t_raise = (-math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
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--~ t_fall = (math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
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--~ posy nach t umstellen
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--~ y = -0.5 * gravity * t * t + vel.y * t + pos.y
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--~ 0 = -0.5 * gravity * t * t + vel.y * t + pos.y - y
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--~ t = (-vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / (-gravity)
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--~ t = (vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
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--~ t_up = (vel.y - math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
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--~ t_down = (vel.y + math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
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--~ posx(t) = vel.x * t + pos.x
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--~ posz(t) = vel.z * t + pos.z
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@ -623,17 +634,19 @@ local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount)
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local pointcount = 0
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-- the height of the 45° angle point
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local yswitch = 0.5 * (vel.y * vel.y - 1) / gravity + pos.y
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local yswitch = -0.5 * (vel.x * vel.x + vel.z * vel.z - vel.y * vel.y)
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/ gravity + pos.y
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local t_fall_start = (vel.y + 1) / gravity
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local t_raise_end = (vel.y - 1) / gravity
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-- the times of the 45° angle point
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t_raise_end = (-math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
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t_fall_start = (math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
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if t_fall_start > 0 then
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-- the right 45° angle point wasn't passed yet
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if t_raise_end > 0 then
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-- put points from before the 45° angle
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for y = math.ceil(pos.y), math.floor(yswitch +.5) do
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local t = -vel.y
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- math.sqrt(vel.y * vel.y - 2 * gravity * (y - pos.y)) / gravity
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local t = (vel.y -
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math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
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local p = {
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x = math.floor(vel.x * t + pos.x +.5),
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y = y,
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@ -684,10 +697,15 @@ local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount)
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end
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end
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-- put points from after the 45° angle
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local y = math.floor(math.min(yswitch, pos.y) +.5)
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local y = yswitch
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if vel.y < 0
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and pos.y < yswitch then
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y = pos.y
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end
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local y = math.floor(y +.5)
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while pointcount < max_pointcount do
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local t = -vel.y
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+ math.sqrt(vel.y * vel.y + 2 * gravity * (pos.y - y)) / gravity
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local t = (vel.y +
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math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
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local p = {
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x = math.floor(vel.x * t + pos.x +.5),
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y = y,
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@ -699,11 +717,26 @@ local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount)
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y = y-1
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end
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end
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--~ local ps = vector.throw_parabola(player:getpos(), player:get_look_dir(),
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--~ 0.03, 80, true)
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--~ for i = 1,#ps do
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--~ minetest.set_node(ps[i], ps[i])
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--[[
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minetest.override_item("default:axe_wood", {
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on_use = function(_, player)
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local dir = player:get_look_dir()
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local pos = player:getpos()
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local grav = 0.03
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local ps = vector.throw_parabola(pos, dir, grav, 80, true)
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for i = 1,#ps do
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minetest.set_node(ps[i], ps[i])
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end
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--~ for t = 0,50,3 do
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--~ local p = {
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--~ x = dir.x * t + pos.x,
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--~ y = -0.5*grav*t*t + dir.y*t + pos.y,
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--~ z = dir.z * t + pos.z
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--~ }
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--~ minetest.set_node(p, {name="default:sandstone"})
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--~ end
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end,
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})--]]
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function funcs.throw_parabola(pos, vel, gravity, point_count, thicken)
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local waypoints = {}
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