PathSlide.cpp

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/*
 * Copyright 2011 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */
 
#include "include/core/SkBitmap.h"
#include "include/core/SkCanvas.h"
#include "include/core/SkColorFilter.h"
#include "include/core/SkColorPriv.h"
#include "include/core/SkFont.h"
#include "include/core/SkGraphics.h"
#include "include/core/SkPathBuilder.h"
#include "include/core/SkPathEffect.h"
#include "include/core/SkPathUtils.h"
#include "include/core/SkRegion.h"
#include "include/core/SkShader.h"
#include "include/core/SkTypeface.h"
#include "include/effects/SkGradientShader.h"
#include "include/utils/SkParsePath.h"
#include "src/base/SkTime.h"
#include "src/base/SkUTF.h"
#include "src/core/SkGeometry.h"
#include "tools/fonts/FontToolUtils.h"
#include "tools/timer/TimeUtils.h"
#include "tools/viewer/ClickHandlerSlide.h"
 
#include <stdlib.h>
 
// http://code.google.com/p/skia/issues/detail?id=32
static void test_cubic() {
    SkPoint src[4] = {
        { 556.25000f, 523.03003f },
        { 556.23999f, 522.96002f },
        { 556.21997f, 522.89001f },
        { 556.21997f, 522.82001f }
    };
    SkPoint dst[11];
    dst[10].set(42, -42);   // one past the end, that we don't clobber these
    SkScalar tval[] = { 0.33333334f, 0.99999994f };
 
    SkChopCubicAt(src, dst, tval, 2);
 
#if 0
    for (int i = 0; i < 11; i++) {
        SkDebugf("--- %d [%g %g]\n", i, dst[i].fX, dst[i].fY);
    }
#endif
}
 
static void test_cubic2() {
    const char* str = "M2242 -590088L-377758 9.94099e+07L-377758 9.94099e+07L2242 -590088Z";
    SkPath path;
    SkParsePath::FromSVGString(str, &path);
 
    {
        SkRect r = path.getBounds();
        SkIRect ir;
        r.round(&ir);
        SkDebugf("[%g %g %g %g] [%x %x %x %x]\n",
                SkScalarToDouble(r.fLeft), SkScalarToDouble(r.fTop),
                SkScalarToDouble(r.fRight), SkScalarToDouble(r.fBottom),
                (uint32_t)ir.fLeft, (uint32_t)ir.fTop, (uint32_t)ir.fRight, (uint32_t)ir.fBottom);
    }
 
    SkBitmap bitmap;
    bitmap.allocN32Pixels(300, 200);
 
    SkCanvas canvas(bitmap);
    SkPaint paint;
    paint.setAntiAlias(true);
    canvas.drawPath(path, paint);
}
 
class PathSlide : public ClickHandlerSlide {
    SkScalar fPrevSecs;
    SkScalar fDStroke, fStroke, fMinStroke, fMaxStroke;
    SkPath fPath[6];
    bool fShowHairline;
 
public:
    PathSlide() {
        fPrevSecs = 0;
        fName = "Paths";
    }
 
    void load(SkScalar w, SkScalar h) override {
        test_cubic();
        test_cubic2();
 
        fShowHairline = false;
 
        fDStroke = 1;
        fStroke = 10;
        fMinStroke = 10;
        fMaxStroke = 180;
 
        const SkScalar V = 85;
 
        fPath[0].moveTo(40, 70);
        fPath[0].lineTo(70, 70 + SK_ScalarHalf);
        fPath[0].lineTo(110, 70);
 
        fPath[1].moveTo(40, 70);
        fPath[1].lineTo(70, 70 - SK_ScalarHalf);
        fPath[1].lineTo(110, 70);
 
        fPath[2].moveTo(V, V);
        fPath[2].lineTo(50, V);
        fPath[2].lineTo(50, 50);
 
        fPath[3].moveTo(50, 50);
        fPath[3].lineTo(50, V);
        fPath[3].lineTo(V, V);
 
        fPath[4].moveTo(50, 50);
        fPath[4].lineTo(50, V);
        fPath[4].lineTo(52, 50);
 
        fPath[5].moveTo(52, 50);
        fPath[5].lineTo(50, V);
        fPath[5].lineTo(50, 50);
    }
 
    void drawPath(SkCanvas* canvas, const SkPath& path, SkPaint::Join j) {
        SkPaint paint;
 
        paint.setAntiAlias(true);
        paint.setStyle(SkPaint::kStroke_Style);
        paint.setStrokeJoin(j);
        paint.setStrokeWidth(fStroke);
 
        if (fShowHairline) {
            SkPath fill;
 
            skpathutils::FillPathWithPaint(path, paint, &fill);
            paint.setStrokeWidth(0);
            canvas->drawPath(fill, paint);
        } else {
            canvas->drawPath(path, paint);
        }
 
        paint.setColor(SK_ColorRED);
        paint.setStrokeWidth(0);
        canvas->drawPath(path, paint);
    }
 
    void draw(SkCanvas* canvas) override {
        canvas->clear(0xFFDDDDDD);
 
        canvas->translate(50, 50);
 
        static const SkPaint::Join gJoins[] = {
            SkPaint::kBevel_Join,
            SkPaint::kMiter_Join,
            SkPaint::kRound_Join
        };
 
        for (size_t i = 0; i < std::size(gJoins); i++) {
            canvas->save();
            for (size_t j = 0; j < std::size(fPath); j++) {
                this->drawPath(canvas, fPath[j], gJoins[i]);
                canvas->translate(200, 0);
            }
            canvas->restore();
 
            canvas->translate(0, 200);
        }
    }
 
    bool animate(double nanos) override {
        SkScalar currSecs = TimeUtils::Scaled(1e-9 * nanos, 100);
        SkScalar delta = currSecs - fPrevSecs;
        fPrevSecs = currSecs;
 
        fStroke += fDStroke * delta;
        if (fStroke > fMaxStroke || fStroke < fMinStroke) {
            fDStroke = -fDStroke;
        }
        return true;
    }
 
    Click* onFindClickHandler(SkScalar x, SkScalar y, skui::ModifierKey modi) override {
        fShowHairline = !fShowHairline;
        return nullptr;
    }
 
    bool onClick(ClickHandlerSlide::Click*) override { return false; }
};
 
DEF_SLIDE( return new PathSlide; )
 
//////////////////////////////////////////////////////////////////////////////
 
#include "include/effects/SkCornerPathEffect.h"
#include "src/base/SkRandom.h"
 
class ArcToSlide : public ClickHandlerSlide {
    bool fDoFrame, fDoCorner, fDoConic;
    SkPaint fPtsPaint, fSkeletonPaint, fCornerPaint;
    enum {
        N = 4
    };
    SkPoint fPts[N];
 
public:
    ArcToSlide() : fDoFrame(false), fDoCorner(false), fDoConic(false) {
        SkRandom rand;
        for (int i = 0; i < N; ++i) {
            fPts[i].fX = 20 + rand.nextUScalar1() * 640;
            fPts[i].fY = 20 + rand.nextUScalar1() * 480;
        }
 
        const SkScalar rad = 50;
 
        fPtsPaint.setAntiAlias(true);
        fPtsPaint.setStrokeWidth(15);
        fPtsPaint.setStrokeCap(SkPaint::kRound_Cap);
 
        fCornerPaint.setAntiAlias(true);
        fCornerPaint.setStyle(SkPaint::kStroke_Style);
        fCornerPaint.setStrokeWidth(13);
        fCornerPaint.setColor(SK_ColorGREEN);
        fCornerPaint.setPathEffect(SkCornerPathEffect::Make(rad*2));
 
        fSkeletonPaint.setAntiAlias(true);
        fSkeletonPaint.setStyle(SkPaint::kStroke_Style);
        fSkeletonPaint.setColor(SK_ColorRED);
 
        fName = "ArcTo";
    }
 
    bool onChar(SkUnichar uni) override {
            switch (uni) {
                case '1': this->toggle(fDoFrame); return true;
                case '2': this->toggle(fDoCorner); return true;
                case '3': this->toggle(fDoConic); return true;
                default: break;
            }
            return false;
    }
    void draw(SkCanvas* canvas) override {
        canvas->drawPoints(SkCanvas::kPoints_PointMode, N, fPts, fPtsPaint);
 
        SkPath path;
        this->makePath(&path);
 
        if (fDoCorner) {
            canvas->drawPath(path, fCornerPaint);
        }
 
        canvas->drawPath(path, fSkeletonPaint);
    }
 
protected:
    Click* onFindClickHandler(SkScalar x, SkScalar y, skui::ModifierKey modi) override {
        const SkScalar tol = 4;
        const SkRect r = SkRect::MakeXYWH(x - tol, y - tol, tol * 2, tol * 2);
        for (int i = 0; i < N; ++i) {
            if (r.intersects(SkRect::MakeXYWH(fPts[i].fX, fPts[i].fY, 1, 1))) {
                return new Click([this, i](Click* c) {
                    fPts[i] = c->fCurr;
                    return true;
                });
            }
        }
        return nullptr;
    }
 
    bool onClick(ClickHandlerSlide::Click *) override { return false; }
 
private:
    void makePath(SkPath* path) {
        path->moveTo(fPts[0]);
        for (int i = 1; i < N; ++i) {
            path->lineTo(fPts[i]);
        }
        if (!fDoFrame) {
            path->close();
        }
    }
 
    void toggle(bool& value) {
        value = !value;
    }
};
DEF_SLIDE( return new ArcToSlide; )
 
/////////////
 
class FatStrokeSlide : public ClickHandlerSlide {
    bool fClosed, fShowStroke, fShowHidden, fShowSkeleton, fAsCurves = false;
    int  fJoinType, fCapType;
    float fWidth = 30;
    SkPaint fPtsPaint, fHiddenPaint, fSkeletonPaint, fStrokePaint;
 
    enum {
        N = 4
    };
    SkPoint fPts[N];
 
public:
    FatStrokeSlide()
            : fClosed(false)
            , fShowStroke(true)
            , fShowHidden(false)
            , fShowSkeleton(true)
            , fJoinType(0)
            , fCapType(0) {
        SkRandom rand;
        for (int i = 0; i < N; ++i) {
            fPts[i].fX = 20 + rand.nextUScalar1() * 640;
            fPts[i].fY = 20 + rand.nextUScalar1() * 480;
        }
 
        fPtsPaint.setAntiAlias(true);
        fPtsPaint.setStrokeWidth(10);
        fPtsPaint.setStrokeCap(SkPaint::kRound_Cap);
 
        fHiddenPaint.setAntiAlias(true);
        fHiddenPaint.setStyle(SkPaint::kStroke_Style);
        fHiddenPaint.setColor(0xFF0000FF);
 
        fStrokePaint.setAntiAlias(true);
        fStrokePaint.setStyle(SkPaint::kStroke_Style);
        fStrokePaint.setStrokeWidth(50);
        fStrokePaint.setColor(0x8000FF00);
 
        fSkeletonPaint.setAntiAlias(true);
        fSkeletonPaint.setStyle(SkPaint::kStroke_Style);
        fSkeletonPaint.setColor(SK_ColorRED);
 
        fName = "FatStroke";
    }
    bool onChar(SkUnichar uni) override {
            switch (uni) {
                case '1': this->toggle(fShowSkeleton); return true;
                case '2': this->toggle(fShowStroke); return true;
                case '3': this->toggle(fShowHidden); return true;
                case '4': this->toggle3(fJoinType); return true;
                case '5': this->toggle3(fCapType); return true;
                case '6': this->toggle(fClosed); return true;
                case 'c': this->toggle(fAsCurves); return true;
                case '-': fWidth -= 5; return true;
                case '=': fWidth += 5; return true;
                default: break;
            }
            return false;
    }
 
    void draw(SkCanvas* canvas) override {
        canvas->drawColor(0xFFEEEEEE);
 
        SkPath path;
        this->makePath(&path);
 
        fStrokePaint.setStrokeWidth(fWidth);
        fStrokePaint.setStrokeJoin((SkPaint::Join)fJoinType);
        fStrokePaint.setStrokeCap((SkPaint::Cap)fCapType);
 
        if (fShowStroke) {
            canvas->drawPath(path, fStrokePaint);
        }
        if (fShowHidden) {
            SkPath hidden;
            skpathutils::FillPathWithPaint(path, fStrokePaint, &hidden);
            canvas->drawPath(hidden, fHiddenPaint);
        }
        if (fShowSkeleton) {
            canvas->drawPath(path, fSkeletonPaint);
        }
        canvas->drawPoints(SkCanvas::kPoints_PointMode, N, fPts, fPtsPaint);
    }
 
protected:
    Click* onFindClickHandler(SkScalar x, SkScalar y, skui::ModifierKey modi) override {
        const SkScalar tol = 4;
        const SkRect r = SkRect::MakeXYWH(x - tol, y - tol, tol * 2, tol * 2);
        for (int i = 0; i < N; ++i) {
            if (r.intersects(SkRect::MakeXYWH(fPts[i].fX, fPts[i].fY, 1, 1))) {
                return new Click([this, i](Click* c) {
                    fPts[i] = c->fCurr;
                    return true;
                });
            }
        }
        return nullptr;
    }
 
    bool onClick(ClickHandlerSlide::Click *) override { return false; }
 
private:
    void toggle(bool& value) {
        value = !value;
    }
 
    void toggle3(int& value) {
        value = (value + 1) % 3;
    }
 
    void makePath(SkPath* path) {
        path->moveTo(fPts[0]);
        if (fAsCurves) {
            for (int i = 1; i < N-2; ++i) {
                path->quadTo(fPts[i], (fPts[i+1] + fPts[i]) * 0.5f);
            }
            path->quadTo(fPts[N-2], fPts[N-1]);
        } else {
            for (int i = 1; i < N; ++i) {
                path->lineTo(fPts[i]);
            }
        }
        if (fClosed) {
            path->close();
        }
    }
};
DEF_SLIDE( return new FatStrokeSlide; )
 
static int compute_parallel_to_base(const SkPoint pts[4], SkScalar t[2]) {
    // F = At^3 + Bt^2 + Ct + D
    SkVector A = pts[3] - pts[0] + (pts[1] - pts[2]) * 3.0f;
    SkVector B = (pts[0] - pts[1] - pts[1] + pts[2]) * 3.0f;
    SkVector C = (pts[1] - pts[0]) * 3.0f;
    SkVector DA = pts[3] - pts[0];
 
    // F' = 3At^2 + 2Bt + C
    SkScalar a = 3 * A.cross(DA);
    SkScalar b = 2 * B.cross(DA);
    SkScalar c = C.cross(DA);
 
    int n = SkFindUnitQuadRoots(a, b, c, t);
    SkString str;
    for (int i = 0; i < n; ++i) {
        str.appendf(" %g", t[i]);
    }
    SkDebugf("roots %s\n", str.c_str());
    return n;
}
 
class CubicCurveSlide : public ClickHandlerSlide {
    enum {
        N = 4
    };
    SkPoint fPts[N];
 
public:
    CubicCurveSlide() {
        SkRandom rand;
        for (int i = 0; i < N; ++i) {
            fPts[i].fX = 20 + rand.nextUScalar1() * 640;
            fPts[i].fY = 20 + rand.nextUScalar1() * 480;
        }
        fName = "CubicCurve";
    }
 
    void draw(SkCanvas* canvas) override {
        SkPaint paint;
        paint.setAntiAlias(true);
 
        {
            SkPath path;
            path.moveTo(fPts[0]);
            path.cubicTo(fPts[1], fPts[2], fPts[3]);
            paint.setStyle(SkPaint::kStroke_Style);
            canvas->drawPath(path, paint);
        }
 
        {
            paint.setColor(SK_ColorRED);
            SkScalar t[2];
            int n = compute_parallel_to_base(fPts, t);
            SkPoint loc;
            SkVector tan;
            for (int i = 0; i < n; ++i) {
                SkEvalCubicAt(fPts, t[i], &loc, &tan, nullptr);
                tan.setLength(30);
                canvas->drawLine(loc - tan, loc + tan, paint);
            }
            paint.setStrokeWidth(0.5f);
            canvas->drawLine(fPts[0], fPts[3], paint);
 
            paint.setColor(SK_ColorBLUE);
            paint.setStrokeWidth(6);
            SkEvalCubicAt(fPts, 0.5f, &loc, nullptr, nullptr);
            canvas->drawPoint(loc, paint);
 
            paint.setColor(0xFF008800);
            SkEvalCubicAt(fPts, 1.0f/3, &loc, nullptr, nullptr);
            canvas->drawPoint(loc, paint);
            SkEvalCubicAt(fPts, 2.0f/3, &loc, nullptr, nullptr);
            canvas->drawPoint(loc, paint);
 
       //     n = SkFindCubicInflections(fPts, t);
       //     printf("inflections %d %g %g\n", n, t[0], t[1]);
        }
 
        {
            paint.setStyle(SkPaint::kFill_Style);
            paint.setColor(SK_ColorRED);
            for (SkPoint p : fPts) {
                canvas->drawCircle(p.fX, p.fY, 8, paint);
            }
        }
    }
 
protected:
    Click* onFindClickHandler(SkScalar x, SkScalar y, skui::ModifierKey modi) override {
        const SkScalar tol = 8;
        const SkRect r = SkRect::MakeXYWH(x - tol, y - tol, tol * 2, tol * 2);
        for (int i = 0; i < N; ++i) {
            if (r.intersects(SkRect::MakeXYWH(fPts[i].fX, fPts[i].fY, 1, 1))) {
                return new Click([this, i](Click* c) {
                    fPts[i] = c->fCurr;
                    return true;
                });
            }
        }
        return nullptr;
    }
 
    bool onClick(ClickHandlerSlide::Click *) override { return false; }
};
DEF_SLIDE( return new CubicCurveSlide; )
 
static SkPoint lerp(SkPoint a, SkPoint b, float t) {
    return a * (1 - t) + b * t;
}
 
static int find_max_deviation_cubic(const SkPoint src[4], SkScalar ts[2]) {
    // deviation = F' x (d - a) == 0, solve for t(s)
    // F = At^3 + Bt^2 + Ct + D
    // F' = 3At^2 + 2Bt + C
    // Z = d - a
    // F' x Z = 3(A x Z)t^2 + 2(B x Z)t + (C x Z)
    //
    SkVector A = src[3] + (src[1] - src[2]) * 3 - src[0];
    SkVector B = (src[2] - src[1] - src[1] + src[0]) * 3;
    SkVector C = (src[1] - src[0]) * 3;
    SkVector Z = src[3] - src[0];
    // now forumlate the quadratic coefficients we need to solve for t : F' x Z
    return SkFindUnitQuadRoots(3 * A.cross(Z), 2 * B.cross(Z), C.cross(Z), ts);
}
 
class CubicCurve2Slide : public ClickHandlerSlide {
    enum {
        N = 7
    };
    SkPoint fPts[N];
    SkPoint* fQuad = fPts + 4;
    SkScalar fT = 0.5f;
    bool fShowSub = false;
    bool fShowFlatness = false;
    bool fShowInnerQuads = false;
    SkScalar fScale = 0.75;
 
public:
    CubicCurve2Slide() {
        fPts[0] = { 90, 300 };
        fPts[1] = { 30, 60 };
        fPts[2] = { 250, 30 };
        fPts[3] = { 350, 200 };
 
        fQuad[0] = fPts[0] + SkVector{ 300, 0};
        fQuad[1] = fPts[1] + SkVector{ 300, 0};
        fQuad[2] = fPts[2] + SkVector{ 300, 0};
 
        fName = "CubicCurve2";
    }
 
    bool onChar(SkUnichar uni) override {
            switch (uni) {
                case 's': fShowSub = !fShowSub; break;
                case 'f': fShowFlatness = !fShowFlatness; break;
                case '-': fT -= 1.0f / 32; break;
                case '=': fT += 1.0f / 32; break;
                case 'q': fShowInnerQuads = !fShowInnerQuads; break;
                default: return false;
            }
            fT = std::min(1.0f, std::max(0.0f, fT));
            return true;
    }
 
    static void Dot(SkCanvas* canvas, SkPoint p, SkScalar radius, SkColor c) {
        SkPaint paint;
        paint.setAntiAlias(true);
        paint.setColor(c);
        canvas->drawCircle(p.fX, p.fY, radius, paint);
    }
 
    void draw(SkCanvas* canvas) override {
        SkPaint paint;
        paint.setAntiAlias(true);
 
        {
            paint.setStyle(SkPaint::kStroke_Style);
            SkPath path;
            path.moveTo(fPts[0]);
            path.cubicTo(fPts[1], fPts[2], fPts[3]);
            path.moveTo(fQuad[0]);
            path.quadTo(fQuad[1], fQuad[2]);
            canvas->drawPath(path, paint);
        }
 
        if (fShowSub) {
            paint.setColor(SK_ColorRED);
            paint.setStrokeWidth(1.7f);
            this->showFrame(canvas, fPts, 3, paint);
            this->showFrame(canvas, fQuad, 2, paint);
 
            paint.setColor(SK_ColorBLACK);
            paint.setStyle(SkPaint::kFill_Style);
            SkFont font(ToolUtils::DefaultTypeface(), 20);
            canvas->drawString(SkStringPrintf("t = %g", fT), 20, 20, font, paint);
        }
 
        if (fShowFlatness) {
            this->showFlattness(canvas);
        }
 
        if (fShowInnerQuads) {
            this->showInnerQuads(canvas);
        }
 
        paint.setColor(SK_ColorGRAY);
        paint.setStroke(true);
        canvas->drawPath(SkPathBuilder().addPolygon(fPts, 4, false).detach(), paint);
        canvas->drawPath(SkPathBuilder().addPolygon(fQuad, 3, false).detach(), paint);
 
        for (SkPoint p : fPts) {
            Dot(canvas, p, 7, SK_ColorBLACK);
        }
 
        if ((false)) {
            SkScalar ts[2];
            int n = SkFindCubicInflections(fPts, ts);
            for (int i = 0; i < n; ++i) {
                SkPoint p;
                SkEvalCubicAt(fPts, ts[i], &p, nullptr, nullptr);
                canvas->drawCircle(p.fX, p.fY, 3, paint);
            }
        }
 
    }
 
protected:
    Click* onFindClickHandler(SkScalar x, SkScalar y, skui::ModifierKey modi) override {
        const SkScalar tol = 8;
        const SkRect r = SkRect::MakeXYWH(x - tol, y - tol, tol * 2, tol * 2);
        for (int i = 0; i < N; ++i) {
            if (r.intersects(SkRect::MakeXYWH(fPts[i].fX, fPts[i].fY, 1, 1))) {
                return new Click([this, i](Click* c) {
                    fPts[i] = c->fCurr;
                    return true;
                });
            }
        }
        return nullptr;
    }
 
    bool onClick(ClickHandlerSlide::Click *) override { return false; }
 
private:
    void showFrame(SkCanvas* canvas, const SkPoint pts[], int count, const SkPaint& p) {
        SkPaint paint(p);
        SkPoint storage[3 + 2 + 1];
        SkPoint* tmp = storage;
        const SkPoint* prev = pts;
        for (int n = count; n > 0; --n) {
            for (int i = 0; i < n; ++i) {
                canvas->drawLine(prev[i], prev[i+1], paint);
                tmp[i] = lerp(prev[i], prev[i+1], fT);
            }
            prev = tmp;
            tmp += n;
        }
 
        paint.setColor(SK_ColorBLUE);
        paint.setStyle(SkPaint::kFill_Style);
        int n = tmp - storage;
        for (int i = 0; i < n; ++i) {
            Dot(canvas, storage[i], 4, SK_ColorBLUE);
        }
    }
 
    void showFlattness(SkCanvas* canvas) {
        SkPaint paint;
        paint.setStyle(SkPaint::kStroke_Style);
        paint.setAntiAlias(true);
 
        SkPaint paint2(paint);
        paint2.setColor(0xFF008800);
 
        paint.setColor(0xFF888888);
        canvas->drawLine(fPts[0], fPts[3], paint);
        canvas->drawLine(fQuad[0], fQuad[2], paint);
 
        paint.setColor(0xFF0000FF);
        SkPoint pts[2];
        pts[0] = (fQuad[0] + fQuad[1] + fQuad[1] + fQuad[2])*0.25;
        pts[1] = (fQuad[0] + fQuad[2]) * 0.5;
        canvas->drawLine(pts[0], pts[1], paint);
 
        // cubic
 
        SkVector v0 = (fPts[0] - fPts[1] - fPts[1] + fPts[2]) * fScale;
        SkVector v1 = (fPts[1] - fPts[2] - fPts[2] + fPts[3]) * fScale;
        SkVector v = (v0 + v1) * 0.5f;
 
        SkPoint anchor;
        SkScalar ts[2];
        int n = find_max_deviation_cubic(fPts, ts);
        if (n > 0) {
            SkEvalCubicAt(fPts, ts[0], &anchor, nullptr, nullptr);
            canvas->drawLine(anchor, anchor + v, paint2);
            canvas->drawLine(anchor, anchor + v0, paint);
            if (n == 2) {
                SkEvalCubicAt(fPts, ts[1], &anchor, nullptr, nullptr);
                canvas->drawLine(anchor, anchor + v, paint2);
            }
            canvas->drawLine(anchor, anchor + v1, paint);
        }
        // not sure we can get here
    }
 
    void showInnerQuads(SkCanvas* canvas) {
        auto draw_quad = [canvas](SkPoint a, SkPoint b, SkPoint c, SkColor color) {
            SkPaint paint;
            paint.setAntiAlias(true);
            paint.setStroke(true);
            paint.setColor(color);
 
            canvas->drawPath(SkPathBuilder().moveTo(a).quadTo(b, c).detach(), paint);
        };
 
        SkPoint p0 = SkEvalQuadAt(&fPts[0], fT),
                p1 = SkEvalQuadAt(&fPts[1], fT),
                p2 = lerp(p0, p1, fT);
 
        draw_quad(fPts[0], fPts[1], fPts[2], SK_ColorRED);
        Dot(canvas, p0, 4, SK_ColorRED);
 
        draw_quad(fPts[1], fPts[2], fPts[3], SK_ColorBLUE);
        Dot(canvas, p1, 4, SK_ColorBLUE);
 
        SkPaint paint;
        paint.setAntiAlias(true);
        paint.setColor(0xFF008800);
        canvas->drawLine(p0, p1, paint);
        Dot(canvas, p2, 4, 0xFF00AA00);
    }
};
DEF_SLIDE( return new CubicCurve2Slide; )