koreader/frontend/ui/geometry.lua

--[[--
Utilities for 2D geometry.

All of these apply to full rectangles:

    local Geom = require("ui/geometry")
    Geom:new{ x = 1, y = 0, w = Screen:scaleBySize(100), h = Screen:scaleBySize(200), }

Some behaviour is defined for points:

    Geom:new{ x = 0, y = 0, }

Some behaviour is defined for dimensions:

    Geom:new{ w = Screen:scaleBySize(600), h = Screen:scaleBySize(800), }

Just use it on simple tables that have x, y and/or w, h
or define your own types using this as a metatable.

Where @{ffi.blitbuffer|BlitBuffer} is concerned, a point at (0, 0) means the top-left corner.

]]

local Math = require("optmath")

--[[--
Represents a full rectangle (all fields are set), a point (x & y are set), or a dimension (w & h are set).
@table Geom
]]
local Geom = {
    x = 0, -- left origin
    y = 0, -- top origin
    w = 0, -- width
    h = 0, -- height
}

function Geom:new(o)
    if not o then
        o = {
            x = 0, y = 0,
            w = 0, h = 0,
        }
    end
    setmetatable(o, self)
    self.__index = self
    return o
end

--[[--
Makes a deep copy of itself.
@treturn Geom
]]
function Geom:copy()
    local n = Geom:new()
    n.x = self.x
    n.y = self.y
    n.w = self.w
    n.h = self.h
    return n
end

function Geom:__tostring()
    return self.w.."x"..self.h.."+"..self.x.."+"..self.y
end

--[[--
Offsets rectangle or point by relative values
@int dx x delta
@int dy y delta
]]
function Geom:offsetBy(dx, dy)
    self.x = self.x + dx
    self.y = self.y + dy
    return self
end

--[[--
Offsets rectangle or point to certain coordinates
@int x new x
@int y new y
]]
function Geom:offsetTo(x, y)
    self.x = x
    self.y = y
    return self
end

--[[--
Scales rectangle (top-left corner is rounded down, bottom-right corner is rounded up) or dimension

If a single factor is given, it is applied to both width and height

@int zx scale for x axis
@int zy scale for y axis
]]
function Geom:scaleBy(zx, zy)
    self.w = math.ceil(self.w * zx - 0.001)
    self.h = math.ceil(self.h * (zy or zx) - 0.001)
    return self
end

--[[--
This method also takes care of x and y on top of @{Geom:scaleBy},
c.f., fz_round_rect in MµPDF,
      <https://github.com/ArtifexSoftware/mupdf/blob/d00de0e96a4a5ec90ffc30837d40cd624a6a89e0/source/fitz/geometry.c#L400-L416>

@int zx scale for x axis
@int zy scale for y axis
]]
function Geom:transformByScale(zx, zy)
    self.x = math.floor(self.x * zx + 0.001)
    self.y = math.floor(self.y * (zy or zx) + 0.001)
    self:scaleBy(zx, zy)
end

--[[--
Returns area of itself.

@treturn int
]]
function Geom:area()
    if not self.w or not self.h then
        return 0
    else
        return self.w * self.h
    end
end

--[[--
Enlarges or shrinks dimensions or rectangles

Note that for rectangles the offset stays the same

@int dw width delta
@int dh height delta
]]
function Geom:changeSizeBy(dw, dh)
    self.w = self.w + dw
    self.h = self.h + dh
    return self
end

--[[--
Returns a new outer rectangle that contains both us and a given rectangle

Works for rectangles, dimensions and points

@tparam Geom rect_b
@treturn Geom
]]
function Geom:combine(rect_b)
    return Geom.boundingBox({self, rect_b})
end

--[[--
Returns a new rectangle for the part that we and a given rectangle share

@tparam Geom rect_b
@treturn Geom
]]--
--- @todo what happens if there is no rectangle shared? currently behaviour is undefined.
function Geom:intersect(rect_b)
    local intersected = self:copy()
    if not rect_b or rect_b:area() == 0 then return intersected end

    if self.x < rect_b.x then
        intersected.x = rect_b.x
    end
    if self.y < rect_b.y then
        intersected.y = rect_b.y
    end
    if self.x + self.w < rect_b.x + rect_b.w then
        intersected.w = self.x + self.w - intersected.x
    else
        intersected.w = rect_b.x + rect_b.w - intersected.x
    end
    if self.y + self.h < rect_b.y + rect_b.h then
        intersected.h = self.y + self.h - intersected.y
    else
        intersected.h = rect_b.y + rect_b.h - intersected.y
    end
    return intersected
end

--[[--
Returns true if self does not share any area or edge with rect_b

@tparam Geom rect_b
]]
function Geom:notIntersectWith(rect_b)
    if not rect_b or rect_b:area() == 0 then return true end

    if (self.x >= (rect_b.x + rect_b.w))
    or (self.y >= (rect_b.y + rect_b.h))
    or (rect_b.x >= (self.x + self.w))
    or (rect_b.y >= (self.y + self.h)) then
        return true
    end
    return false
end

--[[--
Returns true if self geom shares area with rect_b.

@tparam Geom rect_b
]]
function Geom:intersectWith(rect_b)
    return not self:notIntersectWith(rect_b)
end

--[[--
Returns true if self does not share any area with rect_b

@tparam Geom rect_b
]]
function Geom:notOpenIntersectWith(rect_b)
    if not rect_b or rect_b:area() == 0 then return true end

    if (self.x > (rect_b.x + rect_b.w))
    or (self.y > (rect_b.y + rect_b.h))
    or (rect_b.x > (self.x + self.w))
    or (rect_b.y > (self.y + self.h)) then
        return true
    end
    return false
end

--[[--
Returns true if self geom shares area or an edge with rect_b.

@tparam Geom rect_b
]]
function Geom:openIntersectWith(rect_b)
    return not self:notOpenIntersectWith(rect_b)
end

--[[--
Set size of dimension or rectangle to size of given dimension/rectangle.

@tparam Geom rect_b
]]
function Geom:setSizeTo(rect_b)
    self.w = rect_b.w
    self.h = rect_b.h
    return self
end

--[[--
Checks whether geom is within current rectangle

Works for dimensions, too. For points, it is basically an equality check.

@tparam Geom geom
]]
function Geom:contains(geom)
    if not geom then return false end

    if self.x <= geom.x
    and self.y <= geom.y
    and self.x + self.w >= geom.x + geom.w
    and self.y + self.h >= geom.y + geom.h
    then
        return true
    end
    return false
end

--[[--
Checks for equality.

Works for rectangles, points, and dimensions.

@tparam Geom rect_b
]]
function Geom:__eq(rect_b)
    if self.x == rect_b.x
    and self.y == rect_b.y
    and self:equalSize(rect_b)
    then
        return true
    end
    return false
end

--[[--
Checks the size of a dimension/rectangle for equality.

@tparam Geom rect_b
]]
function Geom:equalSize(rect_b)
    if self.w == rect_b.w and self.h == rect_b.h then
        return true
    end
    return false
end

--[[--
Checks if our size is smaller than the size of the given dimension/rectangle.

@tparam Geom rect_b
]]
function Geom:__lt(rect_b)
    if self.w < rect_b.w and self.h < rect_b.h then
        return true
    end
    return false
end

--[[--
Checks if our size is smaller or equal to the size of the given dimension/rectangle.
@tparam Geom rect_b
]]
function Geom:__le(rect_b)
    if self.w <= rect_b.w and self.h <= rect_b.h then
        return true
    end
    return false
end

--[[--
Offsets the current rectangle by dx, dy while fitting it into the space
of a given rectangle.

This can also be called with dx=0 and dy=0, which will fit the current
rectangle into the given rectangle.

@tparam Geom rect_b
@int dx
@int dy
]]
function Geom:offsetWithin(rect_b, dx, dy)
    -- check size constraints and shrink us when we're too big
    if self.w > rect_b.w then
        self.w = rect_b.w
    end
    if self.h > rect_b.h then
        self.h = rect_b.h
    end
    -- offset
    self.x = self.x + dx
    self.y = self.y + dy
    -- check offsets
    if self.x < rect_b.x then
        self.x = rect_b.x
    end
    if self.y < rect_b.y then
        self.y = rect_b.y
    end
    if self.x + self.w > rect_b.x + rect_b.w then
        self.x = rect_b.x + rect_b.w - self.w
    end
    if self.y + self.h > rect_b.y + rect_b.h then
        self.y = rect_b.y + rect_b.h - self.h
    end
end

--[[--
Centers the current rectangle at position x and y of a given rectangle.

@tparam Geom rect_b
@int dx
@int dy
]]
function Geom:centerWithin(rect_b, x, y)
    -- check size constraints and shrink us when we're too big
    if self.w > rect_b.w then
        self.w = rect_b.w
    end
    if self.h > rect_b.h then
        self.h = rect_b.h
    end
    -- place to center
    self.x = x - self.w/2
    self.y = y - self.h/2
    -- check boundary
    if self.x < rect_b.x then
        self.x = rect_b.x
    end
    if self.y < rect_b.y then
        self.y = rect_b.y
    end
    if self.x + self.w > rect_b.x + rect_b.w then
        self.x = rect_b.x + rect_b.w - self.w
    end
    if self.y + self.h > rect_b.y + rect_b.h then
        self.y = rect_b.y + rect_b.h - self.h
    end
end

function Geom:shrinkInside(rect_b, dx, dy)
    self:offsetBy(dx, dy)
    return self:intersect(rect_b)
end

--[[--
Returns the Euclidean distance between two geoms.

@tparam Geom rect_b
]]
function Geom:distance(geom)
    return math.sqrt((self.x - geom.x)^2 + (self.y - geom.y)^2)
end

--[[--
Returns the midpoint of two geoms.

@tparam Geom geom
@treturn Geom
]]
function Geom:midpoint(geom)
    return Geom:new{
        x = Math.round((self.x + geom.x) / 2),
        y = Math.round((self.y + geom.y) / 2),
        w = 0, h = 0,
    }
end

--[[--
Returns the center point of this geom.
@treturn Geom
]]
function Geom:center()
    return Geom:new{
        x = self.x + Math.round(self.w / 2),
        y = self.y + Math.round(self.h / 2),
        w = 0, h = 0,
    }
end

--[[--
Resets an existing Geom object to zero.
@treturn Geom
]]
function Geom:clear()
    self.x = 0
    self.y = 0
    self.w = 0
    self.h = 0
    return self
end

--[[--
Checks if a dimension or rectangle is empty.
@treturn bool
]]
function Geom:isEmpty()
    if self.w == 0 or self.h == 0 then
        return true
    end
    return false
end

--[[--
Returns a bounding box which encompasses all passed rectangles.
@tparam Geom rectangles to encompass
@treturn Geom bounding box or nil if no rectangles passed
]]
function Geom.boundingBox(boxes)
    local bounding_box
    for _, geom in ipairs(boxes) do
        -- Easier to work with (x0,x0)+(x1,y1) pairs.
        local box = { x0 = geom.x, y0 = geom.y,
                      x1 = geom.x + geom.w, y1 = geom.y + geom.h }
        if not bounding_box then
            bounding_box = box
        else
            if box.x0 < bounding_box.x0 then bounding_box.x0 = box.x0 end
            if box.y0 < bounding_box.y0 then bounding_box.y0 = box.y0 end
            if box.x1 > bounding_box.x1 then bounding_box.x1 = box.x1 end
            if box.y1 > bounding_box.y1 then bounding_box.y1 = box.y1 end
        end
    end
    if bounding_box then
        return Geom:new{
            x = bounding_box.x0,
            y = bounding_box.y0,
            w = bounding_box.x1 - bounding_box.x0,
            h = bounding_box.y1 - bounding_box.y0,
        }
    end
end

return Geom