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Diffstat (limited to '.config/awesome/quarrel/bezier.lua')
| -rw-r--r-- | .config/awesome/quarrel/bezier.lua | 343 |
1 files changed, 0 insertions, 343 deletions
diff --git a/.config/awesome/quarrel/bezier.lua b/.config/awesome/quarrel/bezier.lua deleted file mode 100644 index 4229961..0000000 --- a/.config/awesome/quarrel/bezier.lua +++ /dev/null @@ -1,343 +0,0 @@ ---------------------------------------------------------------------------- ---- A helper module for computations involving Bézier curves --- --- @author Alex Belykh <albel727@ngs.ru> --- @copyright 2021 Alex Belykh --- @submodule gears.math ---------------------------------------------------------------------------- - -local table_insert = table.insert - -local bezier = {} - ---- Compute the value of a Bézier curve at a given value of the t parameter. --- --- This function evaluates the given curve `B` of an arbitrary degree --- at a given point t. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam number t The value of the t parameter to evaluate the curve at. --- @treturn[1] number The value of `B(t)`. --- @treturn[2] nil `nil`, if c is empty. --- @staticfct gears.math.bezier.curve_evaluate_at --- @see wibox.widget.graph.step_hook -function bezier.curve_evaluate_at(c, t) - local from = c - local tmp = { nil, nil, nil, nil } - while #from > 1 do - for i = 1, #from - 1 do - tmp[i] = from[i] * (1 - t) + from[i + 1] * t - end - tmp[#from] = nil - from = tmp - end - - return from[1] -end - ---- Split a Bézier curve into two curves at a given value of the t parameter. --- --- This function splits the given curve `B` of an arbitrary degree at a point t --- into two curves of the same degree `B_left` and `B_right`, such that --- `B_left(0)=B(0)`, `B_left(1)=B(t)=B_right(0)`, `B_right(1)=B(1)`. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam number t The value of the t parameter to split the curve at. --- @treturn {number,...} The table of control points for `B_left`. --- @treturn {number,...} The table of control points for `B_right`. --- @staticfct gears.math.bezier.curve_split_at --- @see wibox.widget.graph.step_hook -function bezier.curve_split_at(c, t) - local coefs_left, coefs_right = {}, {} - local from = c - local tmp = { nil, nil, nil, nil } - while #from > 0 do - table_insert(coefs_left, from[1]) - table_insert(coefs_right, 1, from[#from]) - for i = 1, #from - 1 do - tmp[i] = from[i] * (1 - t) + from[i + 1] * t - end - tmp[#from] = nil - from = tmp - end - - return coefs_left, coefs_right -end - ---- Get the n-th derivative Bézier curve of a Bézier curve. --- --- This function computes control points for the curve that is --- the derivative of order `n` in `t`, i.e. `B^(n)(t)`, --- of the given curve `B(t)` of an arbitrary degree. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam[opt=1] integer n The order of the derivative to take. --- @treturn[1] {number,...} The table of control points of `B^(n)(t)`. --- @treturn[2] nil If n is less than 0. --- @staticfct gears.math.bezier.curve_derivative --- @see wibox.widget.graph.step_hook -function bezier.curve_derivative(c, n) - n = n or 1 - if n < 0 then - return - end - if n < 1 then - return c - end - local c_len = #c - if c_len < n + 1 then - return {} - end - - local from = c - local tmp = {} - - for l = c_len - 1, c_len - n, -1 do - for i = 1, l do - tmp[i] = (from[i + 1] - from[i]) * l - end - tmp[l + 1] = nil - from = tmp - end - - return from -end - --- This is used instead of plain 0 to try and be compatible --- with objects that implement their own arithmetic via metatables. -local function get_zero(c, zero) - return c and c * 0 or zero -end - ---- Compute the value of the n-th derivative of a Bézier curve ---- at a given value of the t parameter. --- --- This is roughly the same as --- `curve_evaluate_at(curve_derivative(c, n), t)`, but the latter --- would throw errors or return nil instead of 0 in some cases. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam number t The value of the t parameter to compute the derivative at. --- @tparam[opt=1] integer n The order of the derivative to take. --- @tparam[opt=nil] number|nil zero The value to return if c is empty. --- @treturn[1] number The value of `B^(n)(t)`. --- @treturn[2] nil nil, if n is less than 0. --- @treturn[3] number|nil The value of the zero parameter, if c is empty. --- @staticfct gears.math.bezier.curve_derivative_at --- @see wibox.widget.graph.step_hook -function bezier.curve_derivative_at(c, t, n, zero) - local d = bezier.curve_derivative(c, n) - if not d then - return - end - - return bezier.curve_evaluate_at(d, t) or get_zero(c[1], zero) -end - ---- Compute the value of the 1-st derivative of a Bézier curve at t=0. --- --- This is the same as `curve_derivative_at(c, 0)`, but since it's particularly --- computationally simple and useful in practice, it has its own function. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam[opt=nil] number|nil zero The value to return if c is empty. --- @treturn[1] number The value of `B'(0)`. --- @treturn[2] number|nil The value of the zero parameter, if c is empty. --- @staticfct gears.math.bezier.curve_derivative_at_zero --- @see wibox.widget.graph.step_hook -function bezier.curve_derivative_at_zero(c, zero) - local l = #c - if l < 2 then - return get_zero(c[1], zero) - end - return (c[2] - c[1]) * (l - 1) -end - ---- Compute the value of the 1-st derivative of a Bézier curve at t=1. --- --- This is the same as `curve_derivative_at(c, 1)`, but since it's particularly --- computationally simple and useful in practice, it has its own function. --- --- @tparam {number,...} c The table of control points of the curve. --- @tparam[opt=nil] number|nil zero The value to return if c is empty. --- @treturn[1] number The value of `B'(1)`. --- @treturn[2] number|nil The value of the zero parameter, if c is empty. --- @staticfct gears.math.bezier.curve_derivative_at_one --- @see wibox.widget.graph.step_hook -function bezier.curve_derivative_at_one(c, zero) - local l = #c - if l < 2 then - return get_zero(c[1], zero) - end - return (c[l] - c[l - 1]) * (l - 1) -end - ---- Get the (n+1)-th degree Bézier curve, that has the same shape as --- a given n-th degree Bézier curve. --- --- Given the control points of a curve B of degree n, this function computes --- the control points for the curve Q, such that `Q(t) = B(t)`, and --- Q has the degree n+1, i.e. it has one control point more. --- --- @tparam {number,...} c The table of control points of the curve B. --- @treturn {number,...} The table of control points of the curve Q. --- @staticfct gears.math.bezier.curve_elevate_degree --- @see wibox.widget.graph.step_hook -function bezier.curve_elevate_degree(c) - local ret = { c[1] } - local len = #c - - for i = 1, len - 1 do - ret[i + 1] = (i * c[i] + (len - i) * c[i + 1]) / len - end - - ret[len + 1] = c[len] - return ret -end - ---- Get a cubic Bézier curve that passes through given points (up to 4). --- --- This function takes up to 4 values and returns the 4 control points --- for a cubic curve --- --- `B(t) = c0\*(1-t)^3 + 3\*c1\*t\*(1-t)^2 + 3\*c2\*t^2\*(1-t) + c3\*t^3`, --- that takes on these values at equidistant values of the t parameter. --- --- If only p0 is given, `B(0)=B(1)=B(for all t)=p0`. --- --- If p0 and p1 are given, `B(0)=p0` and `B(1)=p1`. --- --- If p0, p1 and p2 are given, `B(0)=p0`, `B(1/2)=p1` and `B(1)=p2`. --- --- For 4 points given, `B(0)=p0`, `B(1/3)=p1`, `B(2/3)=p2`, `B(1)=p3`. --- --- @tparam number p0 --- @tparam[opt] number p1 --- @tparam[opt] number p2 --- @tparam[opt] number p3 --- @treturn number c0 --- @treturn number c1 --- @treturn number c2 --- @treturn number c3 --- @staticfct gears.math.bezier.cubic_through_points --- @see wibox.widget.graph.step_hook -function bezier.cubic_through_points(p0, p1, p2, p3) - if not p1 then - return p0, p0, p0, p0 - end - if not p2 then - local c1 = (2 * p0 + p1) / 3 - local c2 = (2 * p1 + p0) / 3 - return p0, c1, c2, p1 - end - if not p3 then - local c1 = (4 * p1 - p2) / 3 - local c2 = (4 * p1 - p0) / 3 - return p0, c1, c2, p2 - end - local c1 = (-5 * p0 + 18 * p1 - 9 * p2 + 2 * p3) / 6 - local c2 = (-5 * p3 + 18 * p2 - 9 * p1 + 2 * p0) / 6 - return p0, c1, c2, p3 -end - ---- Get a cubic Bézier curve with given values and derivatives at endpoints. --- --- This function computes the 4 control points for the cubic curve B, such that --- `B(0)=p0`, `B'(0)=d0`, `B(1)=p3`, `B'(1)=d3`. --- --- @tparam number d0 The value of the derivative at t=0. --- @tparam number p0 The value of the curve at t=0. --- @tparam number p3 The value of the curve at t=1. --- @tparam number d3 The value of the derivative at t=1. --- @treturn number c0 --- @treturn number c1 --- @treturn number c2 --- @treturn number c3 --- @staticfct gears.math.bezier.cubic_from_points_and_derivatives --- @see wibox.widget.graph.step_hook -function bezier.cubic_from_points_and_derivatives(d0, p0, p3, d3) - local c1 = p0 + d0 / 3 - local c2 = p3 - d3 / 3 - return p0, c1, c2, p3 -end - ---- Get a cubic Bézier curve with given values at endpoints and starting ---- derivative, while minimizing (an approximation of) the stretch energy. --- --- This function computes the 4 control points for the cubic curve B, such that --- `B(0)=p0`, `B'(0)=d0`, `B(1)=p3`, and --- the integral of `(B'(t))^2` on `t=[0,1]` is minimal. --- (The actual stretch energy is the integral of `|B'(t)|`) --- --- In practical terms this is almost the same as "the curve of shortest length --- connecting given points and having the given starting speed". --- --- @tparam number d0 The value of the derivative at t=0. --- @tparam number p0 The value of the curve at t=0. --- @tparam number p3 The value of the curve at t=1. --- @treturn number c0 --- @treturn number c1 --- @treturn number c2 --- @treturn number c3 --- @staticfct gears.math.bezier.cubic_from_derivative_and_points_min_stretch --- @see wibox.widget.graph.step_hook -function bezier.cubic_from_derivative_and_points_min_stretch(d0, p0, p3) - local c1 = p0 + d0 / 3 - local c2 = (2 * p0 - c1 + 3 * p3) / 4 - return p0, c1, c2, p3 -end - ---- Get a cubic Bézier curve with given values at endpoints and starting ---- derivative, while minimizing (an approximation of) the strain energy. --- --- This function computes the 4 control points for the cubic curve B, such that --- `B(0)=p0`, `B'(0)=d0`, `B(1)=p3`, and --- the integral of `(B''(t))^2` on `t=[0,1]` is minimal. --- --- In practical terms this is almost the same as "the curve of smallest --- speed change connecting given points and having the given starting speed". --- --- @tparam number d0 The value of the derivative at t=0. --- @tparam number p0 The value of the curve at t=0. --- @tparam number p3 The value of the curve at t=1. --- @treturn number c0 --- @treturn number c1 --- @treturn number c2 --- @treturn number c3 --- @staticfct gears.math.bezier.cubic_from_derivative_and_points_min_strain --- @see wibox.widget.graph.step_hook -function bezier.cubic_from_derivative_and_points_min_strain(d, p0, p3) - local c1 = p0 + d / 3 - local c2 = (c1 + p3) / 2 - return p0, c1, c2, p3 -end - ---- Get a cubic Bézier curve with given values at endpoints and starting ---- derivative, while minimizing the jerk energy. --- --- This function computes the 4 control points for the cubic curve B, such that --- `B(0)=p0`, `B'(0)=d0`, `B(1)=p3`, and --- the integral of `(B'''(t))^2` on `t=[0,1]` is minimal. --- --- In practical terms this is almost the same as "the curve of smallest --- acceleration change connecting given points and having the given --- starting speed". --- --- @tparam number d0 The value of the derivative at t=0. --- @tparam number p0 The value of the curve at t=0. --- @tparam number p3 The value of the curve at t=1. --- @treturn number c0 --- @treturn number c1 --- @treturn number c2 --- @treturn number c3 --- @staticfct gears.math.bezier.cubic_from_derivative_and_points_min_jerk --- @see wibox.widget.graph.step_hook -function bezier.cubic_from_derivative_and_points_min_jerk(d, p0, p3) - local c1 = p0 + d / 3 - local c2 = c1 + (p3 - p0) / 3 - return p0, c1, c2, p3 -end - -return bezier - --- vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80 |