From: James Lowe Date: Wed, 10 Aug 2011 22:26:18 +0000 (+0100) Subject: Doc: NR 5.5.4 - Modifing Ties and Slurs X-Git-Tag: release/2.15.9-1~21 X-Git-Url: https://git.donarmstrong.com/?a=commitdiff_plain;h=57bf28a9c6ba1059c368214171be8f4b571533d1;p=lilypond.git Doc: NR 5.5.4 - Modifing Ties and Slurs Put back original description of Beziers. Mine was wrong. Sorry. --- diff --git a/Documentation/notation/changing-defaults.itely b/Documentation/notation/changing-defaults.itely index 1b7614fa95..756e32680b 100644 --- a/Documentation/notation/changing-defaults.itely +++ b/Documentation/notation/changing-defaults.itely @@ -3625,28 +3625,26 @@ Notation Reference: @cindex Bézier curves, control points @cindex control points, Bézier curves -If the shape of the tie or slur which is calculated automatically is not -optimum, the shape may be modified manually by explicitly specifying the -control points required to define the curve needed. - -Ties, slurs and phrasing slurs are drawn as @q{third-order} Bézier -curves which are are defined by four control points. The first and -fourth control points are the start and end points of the curve -respectively, and the two intermediate control points define the -overall shape. - -Animations showing how the curve is drawn can be found on the web, but -the following description may be helpful. The curve starts from the -first control point moving towards the second. As the curve nears and -passes through the second control point it begins to arc towards the -third. The curve continues on towards the the third control point, -again starting to arc as it nears and passes through the third so as to -finish the curve smoothly at the fourth and final control point. The -whole curve is contained in the quadrilateral defined by the four -control points. - -Here is an example of a case where the tie is not optimum (and where the -@code{\tieDown} command would not help). +Ties, slurs and phrasing slurs are drawn as third-order Bézier +curves. If the shape of the tie or slur which is calculated +automatically is not optimum, the shape may be modified manually by +explicitly specifying the four control points required to define +a third-order Bézier curve. + +Third-order or cubic Bézier curves are defined by four control +points. The first and fourth control points are precisely the +starting and ending points of the curve. The intermediate two +control points define the shape. Animations showing how the curve +is drawn can be found on the web, but the following description +may be helpful. The curve starts from the first control point +heading directly towards the second, gradually bending over to +head towards the third and continuing to bend over to head towards +the fourth, arriving there travelling directly from the third +control point. The curve is entirely contained in the +quadrilateral defined by the four control points. + +Here is an example of a case where the tie is not optimum, and +where @code{\tieDown} would not help. @lilypond[verbatim,quote,relative=1] <<