fix: setting width and height to Contain is not preserving aspect ratio of tall images

[saltkid]

fixes #3708, fixes #4407

---

The scaling for "Contain" uses the wrong direct proportion formula for tall images. This is due to the image's aspect being width / height. The original formula scaled_width = scaled_height / aspect expands to

$$\frac{\text{scaled\_width}}{\text{scaled\_height}} = \frac{\text{height}}{\text{width}}$$

which inversely scaled the width of tall images.

The formula is now based on two scaling factors based on the image's dimension relative to the window's. Now, only one computation is needed to cover for all scenarios of computing width instead of having to go through if else branches. Same goes for height.

$$\text{scale\_width} = \frac{\text{window\_width}}{\text{image\_width}}$$ $$\text{scale\_height} = \frac{\text{window\_height}}{\text{image\_height}}$$

These were derived from the principle of direct proportion k=x/y where k is a scaling factor, and x y are the widths of the image and window for example. The larger k is, the larger the window is relative to the image on the width side. Same goes for the height.

Contain needs the minimum scaling factor to ensure both dimensions fit within the window. Cover needs the maximum scaling factor to ensure the image's smaller dimension fits in the window, allowing the larger dimension to crop, as expected. Both of which are the behavior described in the docs.

Example

config used

local wezterm = require("wezterm")
local config = wezterm.config_builder()

config.background = {
	{
		source = {
			Color = "#161616",
		},
		height = "100%",
		width = "100%",
	},
	{
		source = {
			File = os.getenv("HOME") .. "/pictures/wt_bg/center-uniform-0.1/drip yo.jpg",
		},
		width = --[[ VARIABLE ]],
		height =  --[[ VARIABLE ]],
		vertical_align = "Top",
		horizontal_align = "Center",
		repeat_x = "NoRepeat",
		repeat_y = "NoRepeat",
		opacity = 0.2,
	},
}
config.enable_tab_bar = false

return config

1. with both width and height set to "Contain"

old	new

2. both width and height set to "Cover" (no changes)

old	new

art by @AZMC15