diff options
Diffstat (limited to 'macros/luatex/latex/luatodonotes/path_line.lua')
| -rw-r--r-- | macros/luatex/latex/luatodonotes/path_line.lua | 120 |
1 files changed, 120 insertions, 0 deletions
diff --git a/macros/luatex/latex/luatodonotes/path_line.lua b/macros/luatex/latex/luatodonotes/path_line.lua new file mode 100644 index 0000000000..e365a36bf4 --- /dev/null +++ b/macros/luatex/latex/luatodonotes/path_line.lua @@ -0,0 +1,120 @@ +-- Taken from luapower.com (Public domain) +-- +--math for 2D line segments defined as (x1, y1, x2, y2). + +local abs, min, max = math.abs, math.min, math.max + +local distance = require'path_point'.distance +local distance2 = require'path_point'.distance2 + +--evaluate a line at time t using linear interpolation. +--the time between 0..1 covers the segment interval. +local function point(t, x1, y1, x2, y2) + return x1 + t * (x2 - x1), y1 + t * (y2 - y1) +end + +--length of line at time t. +local function length(t, x1, y1, x2, y2) + return t * distance(x1, y1, x2, y2) +end + +--bounding box of line in (x,y,w,h) form. +local function bounding_box(x1, y1, x2, y2) + if x1 > x2 then x1, x2 = x2, x1 end + if y1 > y2 then y1, y2 = y2, y1 end + return x1, y1, x2-x1, y2-y1 +end + +--split line segment into two line segments at time t (t is capped between 0..1). +local function split(t, x1, y1, x3, y3) + t = min(max(t,0),1) + local x2, y2 = point(t, x1, y1, x3, y3) + return + x1, y1, x2, y2, --first segment + x2, y2, x3, y3 --second segment +end + +--intersect infinite line with its perpendicular from point (x, y); return the intersection point. +local function point_line_intersection(x, y, x1, y1, x2, y2) + local dx = x2 - x1 + local dy = y2 - y1 + local k = dx^2 + dy^2 + if k == 0 then return x1, y1 end --line has no length + local k = ((x - x1) * dy - (y - y1) * dx) / k + return x - k * dy, y + k * dx +end + +--return shortest distance-squared from point (x0, y0) to line, plus the touch point, and the time in the line +--where the touch point splits the line. +local function hit(x0, y0, x1, y1, x2, y2) + local x, y = point_line_intersection(x0, y0, x1, y1, x2, y2) + local tx = x2 == x1 and 0 or (x - x1) / (x2 - x1) + local ty = y2 == y1 and 0 or (y - y1) / (y2 - y1) + if tx < 0 or ty < 0 then --intersection occurs outside the segment, closer to the first endpoint + return distance2(x0, y0, x1, y1), x1, y1, 0 + elseif tx > 1 or ty > 1 then --intersection occurs outside the segment, closer to the second endpoint + return distance2(x0, y0, x2, y2), x2, y2, 1 + end + return distance2(x0, y0, x, y), x, y, max(tx, ty) +end + +--intersect line segment (x1, y1, x2, y2) with line segment (x3, y3, x4, y4). +--returns the time on the first line and the time on the second line where intersection occurs. +--if the intersection occurs outside the segments themselves, then t1 and t2 are outside the 0..1 range. +--if the lines are parallel or coincidental then t1 and t2 are infinite. +local function line_line_intersection(x1, y1, x2, y2, x3, y3, x4, y4) + local d = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1) + if d == 0 then return 1/0, 1/0 end --lines are parallel or coincidental + return + ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / d, + ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)) / d +end + +--transform to a quad bezier that advances linearly i.e. the point on the line at t +--best matches the point on the curve at t. +local function to_bezier2(x1, y1, x2, y2) + return + x1, y1, + (x1 + x2) / 2, + (y1 + y2) / 2, + x2, y2 +end + +--transform to a cubic bezier that advances linearly i.e. the point on the line at t +--best matches the point on the curve at t. +local function to_bezier3(x1, y1, x2, y2) + return + x1, y1, + (2 * x1 + x2) / 3, + (2 * y1 + y2) / 3, + (x1 + 2 * x2) / 3, + (y1 + 2 * y2) / 3, + x2, y2 +end + +--parallel line segment at a distance on the right side of a segment. +--use a negative distance for the left side, or reflect the returned points against their respective initial points +local function offset(d, x1, y1, x2, y2) + local dx, dy = -(y2-y1), x2-x1 --normal vector of the same length as original segment + local k = d / distance(x1, y1, x2, y2) --normal vector scale factor + return --normal vector scaled and translated to (x1,y1) and (x2,y2) + x1 + dx * k, y1 + dy * k, + x2 + dx * k, y2 + dy * k +end + +if not ... then require'path_line_demo' end + +return { + point_line_intersection = point_line_intersection, + line_line_intersection = line_line_intersection, + to_bezier2 = to_bezier2, + to_bezier3 = to_bezier3, + offset = offset, + --path API + bounding_box = bounding_box, + point = point, + length = length, + split = split, + hit = hit, +} + |