1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
|
local geom = {}
function geom.on_shape(x,y, drawing, shape)
if shape.mode == 'freehand' then
return geom.on_freehand(x,y, drawing, shape)
elseif shape.mode == 'line' then
return geom.on_line(x,y, drawing, shape)
elseif shape.mode == 'manhattan' then
local p1 = drawing.points[shape.p1]
local p2 = drawing.points[shape.p2]
if p1.x == p2.x then
if x ~= p1.x then return false end
local y1,y2 = p1.y, p2.y
if y1 > y2 then
y1,y2 = y2,y1
end
return y >= y1*0.95 and y <= y2*1.05
elseif p1.y == p2.y then
if y ~= p1.y then return false end
local x1,x2 = p1.x, p2.x
if x1 > x2 then
x1,x2 = x2,x1
end
return x >= x1*0.95 and x <= x2*1.05
else
assert(false)
end
elseif shape.mode == 'polygon' or shape.mode == 'rectangle' or shape.mode == 'square' then
return geom.on_polygon(x,y, drawing, shape)
elseif shape.mode == 'circle' then
local center = drawing.points[shape.center]
return geom.dist(center.x,center.y, x,y) == shape.radius
elseif shape.mode == 'arc' then
local center = drawing.points[shape.center]
local dist = geom.dist(center.x,center.y, x,y)
if dist < shape.radius*0.95 or dist > shape.radius*1.05 then
return false
end
return geom.angle_between(center.x,center.y, x,y, shape.start_angle,shape.end_angle)
elseif shape.mode == 'deleted' then
else
print(shape.mode)
assert(false)
end
end
function geom.on_freehand(x,y, drawing, shape)
local prev
for _,p in ipairs(shape.points) do
if prev then
if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then
return true
end
end
prev = p
end
return false
end
function geom.on_line(x,y, drawing, shape)
local p1,p2
if type(shape.p1) == 'number' then
p1 = drawing.points[shape.p1]
p2 = drawing.points[shape.p2]
else
p1 = shape.p1
p2 = shape.p2
end
if p1.x == p2.x then
if math.abs(p1.x-x) > 5 then
return false
end
local y1,y2 = p1.y,p2.y
if y1 > y2 then
y1,y2 = y2,y1
end
return y >= y1 and y <= y2
end
-- has the right slope and intercept
local m = (p2.y - p1.y) / (p2.x - p1.x)
local yp = p1.y + m*(x-p1.x)
if yp < 0.95*y or yp > 1.05*y then
return false
end
-- between endpoints
local k = (x-p1.x) / (p2.x-p1.x)
return k > -0.05 and k < 1.05
end
function geom.on_polygon(x,y, drawing, shape)
local prev
for _,p in ipairs(shape.vertices) do
if prev then
if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then
return true
end
end
prev = p
end
return geom.on_line(x,y, drawing, {p1=shape.vertices[1], p2=shape.vertices[#shape.vertices]})
end
-- are (x3,y3) and (x4,y4) on the same side of the line between (x1,y1) and (x2,y2)
function geom.same_side(x1,y1, x2,y2, x3,y3, x4,y4)
if x1 == x2 then
return math.sign(x3-x1) == math.sign(x4-x1)
end
if y1 == y2 then
return math.sign(y3-y1) == math.sign(y4-y1)
end
local m = (y2-y1)/(x2-x1)
return math.sign(m*(x3-x1) + y1-y3) == math.sign(m*(x4-x1) + y1-y4)
end
function math.sign(x)
if x > 0 then
return 1
elseif x == 0 then
return 0
elseif x < 0 then
return -1
end
end
function geom.angle_with_hint(x1, y1, x2, y2, hint)
local result = geom.angle(x1,y1, x2,y2)
if hint then
-- Smooth the discontinuity where angle goes from positive to negative.
-- The hint is a memory of which way we drew it last time.
while result > hint+math.pi/10 do
result = result-math.pi*2
end
while result < hint-math.pi/10 do
result = result+math.pi*2
end
end
return result
end
-- result is from -π/2 to 3π/2, approximately adding math.atan2 from Lua 5.3
-- (LÖVE is Lua 5.1)
function geom.angle(x1,y1, x2,y2)
local result = math.atan((y2-y1)/(x2-x1))
if x2 < x1 then
result = result+math.pi
end
return result
end
-- is the line between x,y and cx,cy at an angle between s and e?
function geom.angle_between(ox,oy, x,y, s,e)
local angle = geom.angle(ox,oy, x,y)
if s > e then
s,e = e,s
end
-- I'm not sure this is right or ideal..
angle = angle-math.pi*2
if s <= angle and angle <= e then
return true
end
angle = angle+math.pi*2
if s <= angle and angle <= e then
return true
end
angle = angle+math.pi*2
return s <= angle and angle <= e
end
function geom.dist(x1,y1, x2,y2) return ((x2-x1)^2+(y2-y1)^2)^0.5 end
return geom
|