diff options
| -rw-r--r-- | converter/other/pamtosvg/fit.c | 75 |
1 files changed, 38 insertions, 37 deletions
diff --git a/converter/other/pamtosvg/fit.c b/converter/other/pamtosvg/fit.c index 627435cf..0d8fe534 100644 --- a/converter/other/pamtosvg/fit.c +++ b/converter/other/pamtosvg/fit.c @@ -1177,7 +1177,7 @@ splineLinearEnough(spline_type * const splineP, thisPoint < CURVE_LENGTH(curve); ++thisPoint) { - float const t = CURVE_T(curve, thisPoint); + float const t = CURVE_T(curve, thisPoint); Point const splinePoint = evaluate_spline(*splineP, t); float const a = splinePoint.x - BEG_POINT(*splineP).x; @@ -1263,12 +1263,12 @@ fitWithLine(curve * const curveP) { static spline_type fitOneSpline(curve * const curveP, - Vector const begSlope, - Vector const endSlope, + Vector const begSlope, + Vector const endSlope, at_exception_type * const exceptionP) { /*---------------------------------------------------------------------------- - Return a spline that fits the points of curve *curveP, - with slope 'begSlope' at its beginning and 'endSlope' at its end. + Return a spline that fits the points of curve *curveP, with slope 'begSlope' + at its beginning and 'endSlope' at its end (both are unit vectors). Make it a cubic spline. -----------------------------------------------------------------------------*/ @@ -1285,7 +1285,8 @@ fitOneSpline(curve * const curveP, least-square error in approximating *curveP with the spline. How we do that is a complete mystery to me, but the original author - said to see pp. 57-59 of the Phoenix thesis. I haven't seen that. + said to see pp. 57-59 of the Phoenix thesis. Whatever that is, I + haven't seen it. In our expression of the math here, we use a struct with "beg" and "end" members where the paper uses a matrix with "1" and "2" @@ -1296,18 +1297,22 @@ fitOneSpline(curve * const curveP, The Bernstein polynomials of degree n are defined by B_i^n(t) = { n \choose i } t^i (1-t)^{n-i}, i = 0..n */ - struct VectorPair { + struct VectorBegEndPair { Vector beg; Vector end; }; - struct VectorPair tang; + struct VectorBegEndPair tang; spline_type spline; Vector begVector, endVector; unsigned int i; - struct VectorPair * A; /* malloc'ed array */ + struct VectorBegEndPair * A; /* malloc'ed array */ /* I don't know the meaning of this array, but it is one entry for each point in the curve (A[i] is for the ith point in the curve). + In each entry, the first vector of the pair is a vector in the + direction of the beginning slope of the curve and the other is + in the direction of the end slope of the curve. Their magnitudes + are functions of the ith point. */ struct { struct { float beg; float end; } beg; @@ -1334,13 +1339,12 @@ fitOneSpline(curve * const curveP, X.beg = 0.0; X.end = 0.0; /* initial value */ for (i = 0; i < CURVE_LENGTH(curveP); ++i) { - struct VectorPair * const AP = &A[i]; + struct VectorBegEndPair * const AP = &A[i]; Vector temp, temp0, temp1, temp2, temp3; C.beg.beg += vector_dotProduct(AP->beg, AP->beg); C.beg.end += vector_dotProduct(AP->beg, AP->end); - /* C.end.beg = vector_dotProduct(AP->end, AP->beg) - is done outside of loop */ + C.end.beg += vector_dotProduct(AP->end, AP->beg); C.end.end += vector_dotProduct(AP->end, AP->end); /* Now the right-hand side of the equation in the paper. */ @@ -1360,8 +1364,6 @@ fitOneSpline(curve * const curveP, } free(A); - C.end.beg = C.beg.end; - { float const XCendDet = X.beg * C.end.end - X.end * C.beg.end; float const CbegXDet = C.beg.beg * X.end - C.beg.end * X.beg; @@ -1371,14 +1373,14 @@ fitOneSpline(curve * const curveP, LOG("zero determinant of C matrix"); at_exception_fatal(exceptionP, "zero determinant of C matrix"); } else { - struct { float beg; float end; } alpha; /* constant */ - alpha.beg = XCendDet / CDet; - alpha.end = CbegXDet / CDet; + /* See above for meaning of "alpha */ + float const alphaBeg = XCendDet / CDet; + float const alphaEnd = CbegXDet / CDet; CONTROL1(spline) = vector_sumPoint( - BEG_POINT(spline), vector_scaled(tang.beg, alpha.beg)); + BEG_POINT(spline), vector_scaled(tang.beg, alphaBeg)); CONTROL2(spline) = vector_sumPoint( - END_POINT(spline), vector_scaled(tang.end, alpha.end)); + END_POINT(spline), vector_scaled(tang.end, alphaEnd)); SPLINE_DEGREE(spline) = CUBICTYPE; } } @@ -1568,10 +1570,10 @@ findError(curve * const curveP, worstPoint = 0; for (thisPoint = 0; thisPoint < CURVE_LENGTH(curveP); ++thisPoint) { - Point const curvePoint = CURVE_POINT(curveP, thisPoint); - float const t = CURVE_T(curveP, thisPoint); + Point const curvePoint = CURVE_POINT(curveP, thisPoint); + float const t = CURVE_T(curveP, thisPoint); Point const splinePoint = evaluate_spline(spline, t); - float const thisError = distance(curvePoint, splinePoint); + float const thisError = distance(curvePoint, splinePoint); if (thisError >= worstError) { worstPoint = thisPoint; worstError = thisError; @@ -1599,23 +1601,22 @@ findError(curve * const curveP, static void -setInitialParameterValues(curve * const curveP) { +setCurvePointDistance(curve * const curveP) { /*---------------------------------------------------------------------------- Fill in the 't' values in *curveP. - The t value for point P on a curve is the distance P is along the - curve from the initial point, normalized so the entire curve is - length 1.0 (i.e. t of the initial point is 0.0; t of the final - point is 1.0). + The t value for point P on a curve is the distance P is along the curve + from the initial point, normalized so the entire curve is length 1.0 + (i.e. t of the initial point is 0.0; t of the final point is 1.0). There are a lot of curves that pass through the points indicated by - *curveP, but for practical computation of t, we just take the - piecewise linear locus that runs through all of them. That means - we can just step through *curveP, adding up the distance from one - point to the next to get the t value for each point. + *curveP, but for practical computation of t, we just take the piecewise + linear locus that runs through all of them. That means we can just step + through *curveP, adding up the distance from one point to the next to get + the t value for each point. - This is the "chord-length parameterization" method, which is - described in Plass & Stone. + This is the "chord-length parameterization" method, which is described in + Plass & Stone. -----------------------------------------------------------------------------*/ unsigned int p; @@ -1844,12 +1845,12 @@ fitWithLeastSquares(curve * const curveP, LOG("\nFitting with least squares:\n"); - /* Phoenix reduces the number of points with a "linear spline - technique." But for fitting letterforms, that is - inappropriate. We want all the points we can get. + /* Phoenix reduces the number of points with a "linear spline technique." + But for fitting letterforms, that is inappropriate. We want all the + points we can get. */ - setInitialParameterValues(curveP); + setCurvePointDistance(curveP); if (CURVE_CYCLIC(curveP) && CURVE_LENGTH(curveP) < 4) { unsigned i; |