diff --git a/src/entityToPolyline.js b/src/entityToPolyline.js index 07a24d3..55a728f 100644 --- a/src/entityToPolyline.js +++ b/src/entityToPolyline.js @@ -72,7 +72,7 @@ const interpolateEllipse = (cx, cy, rx, ry, start, end, rotationAngle) => { * @param knots the knot vector * @returns the polyline */ -const interpolateBSpline = (controlPoints, degree, knots, interpolationsPerSplineSegment) => { +export const interpolateBSpline = (controlPoints, degree, knots, interpolationsPerSplineSegment) => { const polyline = [] const controlPointsForLib = controlPoints.map(function (p) { return [p.x, p.y] diff --git a/src/toSVG.js b/src/toSVG.js index 964e229..4472483 100644 --- a/src/toSVG.js +++ b/src/toSVG.js @@ -7,6 +7,7 @@ import getRGBForEntity from './getRGBForEntity' import logger from './util/logger' import rotate from './util/rotate' import rgbToColorAttribute from './util/rgbToColorAttribute' +import toPiecewiseBezier from './util/toPiecewiseBezier' import transformBoundingBoxAndElement from './transformBoundingBoxAndElement' const addFlipXIfApplicable = (entity, { bbox, element }) => { @@ -136,6 +137,32 @@ const arc = (entity) => { return transformBoundingBoxAndElement(bbox, element, entity.transforms) } +export const piecewiseToPaths = (k, controlPoints) => { + const nSegments = (controlPoints.length - 1) / (k - 1) + const paths = [] + for (let i = 0; i < nSegments; ++i) { + const cp = controlPoints.slice(i * (k - 1)) + if (k === 4) { + paths.push(``) + } else if (k === 3) { + paths.push(``) + } + } + return paths +} + +const bezier = (entity) => { + let bbox = new Box2() + entity.controlPoints.forEach(p => { + bbox = bbox.expandByPoint(p) + }) + const k = entity.degree + 1 + const piecewise = toPiecewiseBezier(k, entity.controlPoints, entity.knots) + const paths = piecewiseToPaths(k, piecewise.controlPoints) + let element = `${paths.join('')}` + return transformBoundingBoxAndElement(bbox, element, entity.transforms) +} + /** * Switcth the appropriate function on entity type. CIRCLE, ARC and ELLIPSE * produce native SVG elements, the rest produce interpolated polylines. @@ -150,7 +177,17 @@ const entityToBoundsAndElement = (entity) => { return arc(entity) case 'LINE': case 'LWPOLYLINE': - case 'SPLINE': + case 'SPLINE': { + if ((entity.degree === 2) || (entity.degree === 3)) { + try { + return bezier(entity) + } catch (err) { + return polyline(entity) + } + } else { + return polyline(entity) + } + } case 'POLYLINE': { return polyline(entity) } diff --git a/src/util/insertKnot.js b/src/util/insertKnot.js new file mode 100644 index 0000000..c22dd57 --- /dev/null +++ b/src/util/insertKnot.js @@ -0,0 +1,62 @@ +/** + * Knot insertion is known as "Boehm's algorithm" + * + * https://math.stackexchange.com/questions/417859/convert-a-b-spline-into-bezier-curves + * code adapted from http://preserve.mactech.com/articles/develop/issue_25/schneider.html + */ +export default (k, controlPoints, knots, newKnot) => { + const x = knots + const b = controlPoints + const n = controlPoints.length + let i = 0 + let foundIndex = false + for (let j = 0; j < n + k; j++) { + if (newKnot > x[j] && newKnot <= x[j + 1]) { + i = j + foundIndex = true + break + } + } + if (!foundIndex) { + throw new Error('invalid new knot') + } + + const xHat = [] + for (let j = 0; j < n + k + 1; j++) { + if (j <= i) { + xHat[j] = x[j] + } else if (j === i + 1) { + xHat[j] = newKnot + } else { + xHat[j] = x[j - 1] + } + } + + let alpha + const bHat = [] + for (let j = 0; j < n + 1; j++) { + if (j <= i - k + 1) { + alpha = 1 + } else if (i - k + 2 <= j && j <= i) { + if (x[j + k - 1] - x[j] === 0) { + alpha = 0 + } else { + alpha = (newKnot - x[j]) / (x[j + k - 1] - x[j]) + } + } else { + alpha = 0 + } + + if (alpha === 0) { + bHat[j] = b[j - 1] + } else if (alpha === 1) { + bHat[j] = b[j] + } else { + bHat[j] = { + x: (1 - alpha) * b[j - 1].x + alpha * b[j].x, + y: (1 - alpha) * b[j - 1].y + alpha * b[j].y + } + } + } + return { controlPoints: bHat, knots: xHat } +} diff --git a/src/util/toPiecewiseBezier.js b/src/util/toPiecewiseBezier.js new file mode 100644 index 0000000..9647fd2 --- /dev/null +++ b/src/util/toPiecewiseBezier.js @@ -0,0 +1,62 @@ +import insertKnot from './insertKnot' + +/** + * For a pinned spline, the knots have to be repeated k times + * (where k is the order), at both the beginning and the end + */ +export const checkPinned = (k, knots) => { + // Pinned at the start + for (let i = 1; i < k; ++i) { + if (knots[i] !== knots[0]) { + throw Error(`not pinned. order: ${k} knots: ${knots}`) + } + } + // Pinned at the end + for (let i = knots.length - 2; i > knots.length - k - 1; --i) { + if (knots[i] !== knots[knots.length - 1]) { + throw Error(`not pinned. order: ${k} knots: ${knots}`) + } + } +} + +const multiplicity = (knots, index) => { + let m = 1 + for (let i = index + 1; i < knots.length; ++i) { + if (knots[i] === knots[index]) { + ++m + } else { + break + } + } + return m +} + +/** + * https://saccade.com/writing/graphics/KnotVectors.pdf + * A quadratic piecewise Bézier knot vector with seven control points + * will look like this [0 0 0 1 1 2 2 3 3 3]. In general, in a + * piecewise Bézier knot vector the first k knots are the same, + * then each subsequent group of k-1 knots is the same, + * until you get to the end. + */ +export const computeInsertions = (k, knots) => { + const inserts = [] + let i = k + while (i < knots.length - k) { + const knot = knots[i] + const m = multiplicity(knots, i) + for (let j = 0; j < k - m - 1; ++j) { + inserts.push(knot) + } + i = i + m + } + return inserts +} + +export default (k, controlPoints, knots) => { + checkPinned(k, knots) + const insertions = computeInsertions(k, knots) + return insertions.reduce((acc, tNew) => { + return insertKnot(k, acc.controlPoints, acc.knots, tNew) + }, { controlPoints, knots }) +} diff --git a/test/functional/toBezier.html b/test/functional/toBezier.html new file mode 100644 index 0000000..e6c6412 --- /dev/null +++ b/test/functional/toBezier.html @@ -0,0 +1,16 @@ + + + + + + + + +
+ + + diff --git a/test/functional/toBezier.test.js b/test/functional/toBezier.test.js new file mode 100644 index 0000000..00b171b --- /dev/null +++ b/test/functional/toBezier.test.js @@ -0,0 +1,79 @@ +import React from 'react' +import { render } from 'react-dom' +import { HashRouter } from 'react-router-dom' + +import { interpolateBSpline } from '../../src/entityToPolyline' +import toPiecewiseBezier from '../../src/util/toPiecewiseBezier' +import { piecewiseToPaths } from '../../src/toSVG' + +const controlPoints = [ + { x: 0, y: 0 }, + { x: 10, y: 0 }, + { x: 10, y: 10 }, + { x: 0, y: 10 }, + { x: 0, y: 20 }, + { x: 10, y: 20 } +] +const k = 4 +const knots = [0, 0, 0, 0, 1, 2, 3, 3, 3, 3] +const viewBox = '-1 -21 12 22' + +// const controlPoints = [ +// { x: 0, y: 0 }, +// { x: 122.4178296875701, y: -38.53600688262475 }, +// { x: 77.52934654015353, y: 149.4771453152231 }, +// { x: 200, y: 100 } +// ] +// const k = 3 +// const knots = [0, 0, 0, 0.5, 1, 1, 1] +// const viewBox = '-1 -160 200 200' + +const interpolated0 = interpolateBSpline(controlPoints, k - 1, knots) + +const polylineToPath = (polyline) => { + const d = polyline.reduce(function (acc, point, i) { + acc += (i === 0) ? 'M' : 'L' + acc += point[0] + ',' + point[1] + return acc + }, '') + return +} + +const result = toPiecewiseBezier(k, controlPoints, knots) +const interpolated1 = interpolateBSpline(result.controlPoints, k - 1, result.knots) +const paths = piecewiseToPaths(k, result.controlPoints, k.knots) + +render( +
+ + + {polylineToPath(interpolated0)} + + + + + {polylineToPath(interpolated1)} + + + + + +
+, document.getElementById('contents')) diff --git a/test/functional/toPolylines.test.js b/test/functional/toPolylines.test.js index be09e2a..e2aa270 100644 --- a/test/functional/toPolylines.test.js +++ b/test/functional/toPolylines.test.js @@ -74,7 +74,8 @@ const names = [ 'issue28', 'issue29', 'issue39', - 'issue42' + 'issue42', + 'splineA' ] const dxfs = names.map(name => require(`../resources/${name}.dxf`)) const svgs = dxfs.map(contents => toSVG(new Helper(contents).toPolylines())) diff --git a/test/functional/toSVG.test.js b/test/functional/toSVG.test.js index fdf2151..24161fd 100644 --- a/test/functional/toSVG.test.js +++ b/test/functional/toSVG.test.js @@ -29,7 +29,8 @@ const names = [ 'issue28', 'issue29', 'issue39', - 'issue42' + 'issue42', + 'splineA' ] const dxfs = names.map(name => require(`../resources/${name}.dxf`)) const svgs = dxfs.map(contents => new Helper(contents).toSVG()) diff --git a/test/functional/webpack.config.js b/test/functional/webpack.config.js index 36f69c7..5da6d98 100644 --- a/test/functional/webpack.config.js +++ b/test/functional/webpack.config.js @@ -17,6 +17,11 @@ module.exports = { `webpack-dev-server/client?http://localhost:${port}`, 'webpack/hot/dev-server', path.resolve(__dirname, 'toSVG.test.js') + ], + 'toBezier.test': [ + `webpack-dev-server/client?http://localhost:${port}`, + 'webpack/hot/dev-server', + path.resolve(__dirname, 'toBezier.test.js') ] }, output: { diff --git a/test/resources/splineA.dxf b/test/resources/splineA.dxf new file mode 100644 index 0000000..b86254a --- /dev/null +++ b/test/resources/splineA.dxf @@ -0,0 +1,2758 @@ +999 +dxfrw 0.6.3 + 0 +SECTION + 2 +HEADER + 9 +$ACADVER + 1 +AC1021 + 9 +$DWGCODEPAGE + 3 +ANSI_1252 + 9 +$INSBASE + 10 +0 + 20 +0 + 30 +0 + 9 +$EXTMIN + 10 +-40.01848471883363 + 20 +-12.5 + 30 +0 + 9 +$EXTMAX + 10 +312.5 + 20 +211.7119175361894 + 30 +0 + 9 +$LIMMIN + 10 +0 + 20 +0 + 9 +$LIMMAX + 10 +420 + 20 +297 + 9 +$ORTHOMODE + 70 + 0 + 9 +$REGENMODE + 70 + 1 + 9 +$FILLMODE + 70 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diff --git a/test/unit/insertKnot.test.js b/test/unit/insertKnot.test.js new file mode 100644 index 0000000..9c5199a --- /dev/null +++ b/test/unit/insertKnot.test.js @@ -0,0 +1,35 @@ +import expect from 'expect' + +import insertKnot from '../../src/util/insertKnot' + +describe('Insert knot', () => { + it('throws error if knot is invalid', () => { + const controlPoints = [ + { x: 0, y: 0 }, + { x: 10, y: 0 }, + { x: 10, y: 10 }, + { x: 0, y: 10 }, + { x: 0, y: 20 }, + { x: 10, y: 20 } + ] + const k = 4 + const knots = [0, 0, 0, 0, 1, 2, 3, 3, 3, 3] + expect(() => { + insertKnot(k, controlPoints, knots, 4) + }).toThrow(/^invalid new knot$/) + expect(() => { + insertKnot(k, controlPoints, knots, -1) + }).toThrow(/^invalid new knot$/) + const newSpline = insertKnot(k, controlPoints, knots, 1) + expect(newSpline.controlPoints).toEqual([ + { x: 0, y: 0 }, + { x: 10, y: 0 }, + { x: 10, y: 5 }, + { x: 6.666666666666668, y: 10 }, + { x: 0, y: 10 }, + { x: 0, y: 20 }, + { x: 10, y: 20 } + ]) + expect(newSpline.knots).toEqual([0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3]) + }) +}) diff --git a/test/unit/toPiecewiseBezier.test.js b/test/unit/toPiecewiseBezier.test.js new file mode 100644 index 0000000..319d171 --- /dev/null +++ b/test/unit/toPiecewiseBezier.test.js @@ -0,0 +1,47 @@ +import expect from 'expect' + +import { checkPinned, computeInsertions } from '../../src/util/toPiecewiseBezier' + +describe('Spline conversion to piecewise bezier', () => { + it('checks that the spline is pinned', () => { + expect(checkPinned(4, [0, 0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 1])) + expect(() => { + checkPinned(4, [0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,0.2,0.4,0.6000000000000001,0.8,1,1,1,1$/) + expect(() => { + checkPinned(4, [0, 1, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,1,0,0,0.2,0.4,0.6000000000000001,0.8,1,1,1,1$/) + expect(() => { + checkPinned(4, [0, 0, 1, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,1,0,0.2,0.4,0.6000000000000001,0.8,1,1,1,1$/) + expect(() => { + checkPinned(4, [0, 0, 0, 1, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,1,0.2,0.4,0.6000000000000001,0.8,1,1,1,1$/) + + expect(() => { + checkPinned(4, [0, 0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 0.9, 1, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,0,0.2,0.4,0.6000000000000001,0.8,0.9,1,1,1$/) + expect(() => { + checkPinned(4, [0, 0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 0.9, 1, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,0,0.2,0.4,0.6000000000000001,0.8,1,0.9,1,1$/) + expect(() => { + checkPinned(4, [0, 0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 0.9, 1]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,0,0.2,0.4,0.6000000000000001,0.8,1,1,0.9,1$/) + expect(() => { + checkPinned(4, [0, 0, 0, 0, 0.2, 0.4, 0.6000000000000001, 0.8, 1, 1, 1, 0.9]) + }).toThrow(/^not pinned. order: 4 knots: 0,0,0,0,0.2,0.4,0.6000000000000001,0.8,1,1,1,0.9$/) + }) + + it('computes the knots to be inserted for a piecewise bezier', () => { + expect(computeInsertions(4, [0, 0, 0, 0, 1, 2, 2, 2, 2])) + .toEqual([1, 1]) + expect(computeInsertions(4, [0, 0, 0, 0, 0.5, 2, 2, 2, 2])) + .toEqual([0.5, 0.5]) + expect(computeInsertions(4, [0, 0, 0, 0, 0.5, 0.5, 0.5, 2, 2, 2, 2])) + .toEqual([]) + expect(computeInsertions(3, [0, 0, 0, 1, 1, 2, 2, 2])) + .toEqual([]) + expect(computeInsertions(3, [0, 0, 0, 1, 2, 2, 2])) + .toEqual([1]) + }) +})