Normally WordPad (at least here) uses the Calibri font unless told otherwise.
]]>The problem with posting that I was having appears to be that the text produced by Copilot when copied from the web page and pasted into WordPad was typesetting the names of the variables in italics. I think it was using the special ISO/IEC 10646 / Unicode special mathematical characters. The software under the bonnet (under the hood in American English) in this forum was giving up when it met such a character.
The text in Copilot itself uses italics for B, P, and t.
]]>William wrote:Fontmaking software like TrueType and OpenType …
Huh?
Ah yes, I had not noticed that! Arrgh!
You know of course, but for completeness TrueType and OpenType are fontmaking format specifications. Fontmaking software applies those format specifications.
]]>Fontmaking software like TrueType and OpenType …
Huh?
]]>t is the parameter that varies from 0 to 1, tracing the curve.
This formula ensures that the curve starts at P0, is pulled toward P1, and finally reaches P2.
The influence of P1 on the curvature is strongest when t = 0.5, making it a critical component in defining how smooth or sharp the curve appears.
[The next paragraph from Copilot has been deleted as it was incorrect, as mentioned in a post later in this thread.]
]]>I had in mind asking Copilot again and doing a Print Screen and then adding a png image to this thread.
]]>[Note by WJGO P0, P1, P2 are meant to be P with a subscript 0, P with a subscript 1, P with a subscript 2. Subscripts are used in the original but not in this transcript.]
I’m having difficulty with those subscript numerals, too! This is the best I can do:
A quadratic Bézier curve is a parametric curve defined using three control points. The formula for the curve is:
B(t) = (1 − t)²P₀ + 2(1 − t)tP₁ + t²P₂
where
• P₀, P₁, and P₂ are the control points
• t is the parameter ranging from 0 to 1This formula ensures a smooth curve that starts at P₀, moves toward P₁ as an intermediate guide, and ends at P₂. Quadratic Bézier curves are commonly used in computer graphics, font rendering, and animations.
Please explain the mathematical formula for a Quadratic Bézier Curve as used in drawing glyphs in fontmaking software.
[Copilot]
Ah, the Quadratic Bézier Curve—a foundational tool in digital typography and glyph design! Its formula is quite elegant and allows for smooth, precise curves, which are essential in fontmaking.
A Quadratic Bézier Curve is defined mathematically as:
[Note by WJGO P0, P1, P2 are meant to be P with a subscript 0, P with a subscript 1, P with a subscript 2. Subscripts are used in the original but not in this transcript.]
IS THE FORMULA THE ISSUE?
where:
]]>