WORKING WITH S YMBOLIC REPRES ENTATIONS in Font

Creator PDF-417 2d barcode in Font WORKING WITH S YMBOLIC REPRES ENTATIONS

Listing 12-9. Visual Elements and Sizes for the Visual Symbolic Differentiation Application type VisualElement = | Symbol of string * ExprSize | Power of VisualElement * VisualElement * ExprSize | Sequence of VisualElement list * ExprSize | Fraction of VisualElement * VisualElement * ExprSize member self.Size = match self with | Symbol (_, size) | Power (_, _, size) | Sequence (_, size) | Fraction (_, _, size) -> size member self.Height = self.Size.height member self.Width = self.Size.width member self.Midline = self.Size.midline and ExprSize = { width: int;

height: int;

midline: int; }

member self.CenterOnMidline size x y = x + (size.width-self.width)/2, y + (size.midline-self.midline) member self.Frac size opt = { width = max self.width size.width; height = self.height + size.height + self.FracSepHeight opt; midline = self.height + (self.FracSepHeight opt)/2; } member self.FracSepHeight (opt: RenderOptions) = max (int (opt.Pen.Width*5.0f)) 4 member self.AddPower (e: VisualElement) = { width = self.width + e.Width; height = self.height + e.Height; midline = self.midline + e.Height; } static member { width height midline ExpandOne (size: ExprSize) (e: VisualElement) = = size.width + e.Width; = max size.height e.Height; = max size.midline e.Midline; }

member self.Expand (exprs: VisualElement list) = List.fold_left ExprSize.ExpandOne self exprs static member Seq (exprs: VisualElement list) = List.fold_left ExprSize.ExpandOne ExprSize.Zero exprs static member Zero = { width=0; height=0; midline=0; }

This size value encodes the dimensions (width and height in pixels) of the related visual expression and is managed through the ExprSize type, which provides various members to compute precise dimensions. Basically, this is the type that handles the gory details of putting small visuals together to compose a large expression and manages how and where these small visuals should be placed. The main guideline is to align these visuals on a line (measured from the top of the expression in pixels and stored in the midline field), as depicted in Figure 12-3.

Figure 12-3. Expressions and their sizes The darker rectangles in this figure denote arbitrary expressions, whereas the lighter rectangle marks the dimensions of the parent expression aligned on the midline.

Listing 12-10 shows the type VisualExpr that carries the main visual element and the rendering options that were used to produce it. This type also provides the method OfExpr to build a VisualExpr from an Expr.

Listing 12-10. Visual Expressions for the Visual Symbolic Differentiation Application type VisualExpr = { Expression : VisualElement;

RenderOptions: RenderOptions; }

static member OfExpr (opt: RenderOptions) e = use bmp = new Bitmap(100, 100, PixelFormat.Format32bppArgb) use gra = Graphics.FromImage(bmp) let sizeOf (opt: RenderOptions) s = use sFormat = new StringFormat(StringFormat.GenericTypographic) let font = if opt.IsSuper then opt.SmallFont else opt.NormalFont let size = gra.MeasureString(s, font, PointF(0.0f, 0.0f), sFormat) let height = int size.Height { width = int size.Width + 2; height = height; midline = height/2; } let precPow = 70 let precProd1, precProd2 = 30, 40 let precAdd1, precAdd2 = 10, 11 let precStart = 5 let precNeg1, precNeg2 = 1, 20 let sym opt s = Symbol (s, sizeOf opt s) let applyPrec opt pprec prec exprs (size: ExprSize) = if pprec > prec then sym opt "(" :: exprs @ [sym opt ")"], size.Expand [sym opt "("; sym opt ")"] else exprs, size let mkSequence opt pprec prec exprs = let size = ExprSize.Seq exprs let exprs, size = applyPrec opt pprec prec exprs size Sequence (exprs, size) let rec expFunc opt f par = let f' = sym opt f let exprs' = [sym opt "("; exp opt precStart par; sym opt ")"] Sequence (f' :: exprs', f'.Size.Expand exprs') and exp (opt: RenderOptions) prec = function | Num n -> let s = BigNum.to_string n in Symbol (s, sizeOf opt s) | Var v -> Symbol (v, sizeOf opt v)