basic bezier curves with sample

examples/bezier/.gitignore

@@ -0,0 +1,14 @@
+.dub
+docs.json
+__dummy.html
+docs/
+bezier.so
+bezier.dylib
+bezier.dll
+bezier.a
+bezier.lib
+bezier-test-*
+*.exe
+*.o
+*.obj
+*.lst

examples/bezier/dub.json

@@ -0,0 +1,32 @@
+{
+	"name": "bezier",
+	"description": "dlangui bezier curves samples",
+	"license": "Boost",
+
+	"targetPath": "bin",
+    "targetType": "executable",
+    "targetName": "bezier",
+
+    "sourceFiles-windows-x86-dmd": ["$PACKAGE_DIR/../../src/win_app.def"],
+
+    "dependencies": {
+        "dlangui": {"path": "../../"}
+    },
+    "configurations" : [
+        {
+            "name" : "default"
+        }, 
+        {
+            "name" : "sdl",
+            "subConfigurations" : {
+                "dlangui" : "sdl"
+            }
+        },
+        {
+            "name" : "x11",
+            "subConfigurations" : {
+                "dlangui" : "x11"
+            }
+        }
+    ]
+}

examples/bezier/source/app.d

@@ -0,0 +1,230 @@
+module app;
+
+static assert(ENABLE_OPENGL, "All bezier samples in this module using 
+    floating point drawing functions which is not supported in minimal config");
+
+import dlangui;
+
+import std.algorithm.comparison;
+
+mixin APP_ENTRY_POINT;
+
+// helper for scaling relative to average 96dpi FullHD, IDK but maybe a bad idea after all
+T scaledByDPI(T)(T val) {
+    return val *= (SCREEN_DPI()/cast(T)96);
+}
+
+/// Entry point for dlangui based application
+extern (C) int UIAppMain(string[] args) {
+    // portrait "mode" window
+    Window window = Platform.instance.createWindow("Bezier curves", null, WindowFlag.Resizable, 480.scaledByDPI, 600.scaledByDPI);
+    window.mainWidget = new BezierSamples();
+    window.show();
+    return Platform.instance.enterMessageLoop();
+}
+
+class BezierSamples : VerticalLayout {
+
+    this() {
+        this(null);
+    }
+    this(string id) {
+        super(id);
+        addChild(new CubicTraceSample);
+        addChild(new FlattenCubicSample);
+        addChild(new ColoredCubicTraceSample);
+        addChild(new FlattenCubicGuidesSample);
+        addChild(new FlattenQuadraticSample);
+    }
+
+    override bool animating() { return true; }
+}
+
+
+abstract class SampleCanvas : CanvasWidget {
+
+    dstring _sampleName = "Bezier sample";
+    static immutable vec2[] _controlPointsDefaultRatios = [vec2(0,0.2), vec2(0.2,0.2), vec2(0.8,0.8), vec2(1,0.8)];
+    static immutable vec2[] _controlPointsQuadratic = [vec2(0.2,0.8), vec2(0.7,0.4), vec2(0.3,0.2)];
+
+    this() {
+        fillHorizontal();
+        auto p = 5.scaledByDPI;
+        margins(Rect(p, p, p, p));
+        p = 15.scaledByDPI;
+        padding(Rect(p, p, p, p));
+        minHeight = 250.scaledByDPI;
+    }
+
+    dstring sampleName() { return _sampleName; }
+
+    override protected void measuredContent(int parentWidth, int parentHeight, int contentWidth, int contentHeight) {
+        _measuredWidth = max(minHeight, contentWidth);
+        _measuredHeight = minHeight;
+    }
+
+    protected void drawText(DrawBuf buf, Rect rc, dstring text) {
+        FontRef font = font();
+        Point sz = font.textSize(text);
+        applyAlign(rc, sz, Align.HCenter, Align.Bottom );
+        font.drawText(buf, rc.left, rc.top, text, textColor, 4, 0, textFlags);
+    }
+
+    protected void calcRectSize(const vec2[] controlPoints, vec2[] result) {
+        assert(result.length >= controlPoints.length);
+        auto r = _pos;
+        applyMargins(r);
+        applyPadding(r);
+        vec2 pos = vec2(r.left, r.top);
+        vec2 size = vec2(r.width, r.height);
+        result[] = controlPoints[]; // copy points
+        result[0] = result[0].mul(size) + pos;
+        result[1] = result[1].mul(size) + pos;
+        result[2] = result[2].mul(size) + pos;
+        if(controlPoints.length > 3)
+        result[3] = result[3].mul(size) + pos;
+    }
+
+    // override to draw
+    override void doDraw(DrawBuf buf, Rect rc) {
+    }
+}
+
+class CubicTraceSample : SampleCanvas {
+    this() {
+        _sampleName = "Cubic bezier curve drawn with ellipses (slow, high overdraw)";
+    }
+    override void doDraw(DrawBuf buf, Rect rc) {
+        vec2[4] points;
+        calcRectSize(_controlPointsDefaultRatios, points);
+        auto len = (points[0]-points[3]).magnitude;
+        auto interval = 1f/len;
+        auto step = interval;
+        // evaluate normal bezier curve and trace with circles
+        foreach ( i ; 0..len ) {
+            auto b = bezierCubic(points, interval); 
+            interval+=step;
+            buf.drawEllipseF(b.x, b.y, 3, 3, 0, Color.black, Color.black);
+        }
+        drawText(buf,rc, sampleName());
+    }
+}
+
+class FlattenCubicSample : SampleCanvas {
+    this() {
+        _sampleName = "Flattened cubic bezier curve drawn with lines (fast)";
+    }
+    override void doDraw(DrawBuf buf, Rect rc) {
+        vec2[4] points;
+        calcRectSize(_controlPointsDefaultRatios, points);
+        enum segments = 10;
+        auto lines = flattenBezierCubic(points, segments);
+        buf.polyLineF(lines, 3f.scaledByDPI, Color.black);
+        drawText(buf,rc, sampleName());
+    }
+}
+
+class ColoredCubicTraceSample : SampleCanvas {
+    this() {
+        _sampleName = "Simple colored cubic bezier curve drawn with ellipsises";
+    }
+    override void doDraw(DrawBuf buf, Rect rc) {
+        vec2[4] points;
+        calcRectSize(_controlPointsDefaultRatios, points);
+        auto len = (points[0]-points[3]).magnitude;
+        auto interval = 1/len;
+        auto step = interval;
+        // evaluate normal bezier curve and trace with circles
+        foreach ( i ; 0..len ) {
+            auto b = bezierCubic(points, interval); 
+            interval+=step;
+            buf.drawEllipseF(b.x, b.y, 3, 3, 0, COLOR_TRANSPARENT, lerpColor01(Color.blue, Color.red, interval));
+        }
+        drawText(buf,rc, sampleName());
+    }
+
+    // clamp to [0,1] and lerp color
+    static uint lerpColor01(uint a, uint b, float ratio) {
+        ratio = clamp(ratio, 0, 1);
+        return blendARGB(b, a, cast(uint)(ratio * 255));
+    }
+}
+
+class FlattenCubicGuidesSample : SampleCanvas {
+    this() {
+        _sampleName = "Flattened cubic bezier curve with direction and normal vectors";
+    }
+    override void doDraw(DrawBuf buf, Rect rc) {
+        vec2[4] points;
+        calcRectSize(_controlPointsDefaultRatios, points);
+        enum segmentsCount = 10;
+        auto lines = flattenBezierCubic(points, segmentsCount);
+        drawCubicControlsGuides(buf, points);
+        buf.polyLineF(lines, 3f.scaledByDPI, Color.black);
+        drawCubicSegmentsNormDir(buf, points, segmentsCount, lines, true, true);
+        drawText(buf,rc, sampleName());
+    }
+}
+
+class FlattenQuadraticSample : SampleCanvas {
+    this() {
+        _sampleName = "Flattened quadratic bezier curve";
+    }
+    override void doDraw(DrawBuf buf, Rect rc) {
+        vec2[3] points;
+        calcRectSize(_controlPointsQuadratic, points);
+
+        // guide lines
+        buf.drawLineF(points[0], points[1], 1, Color.dark_gray);
+        buf.drawLineF(points[1], points[2], 1, Color.dark_gray);
+        
+
+        enum segmentCount = 10;
+        auto lines = flattenBezierQuadratic(points, segmentCount);
+        buf.polyLineF(lines, 3f.scaledByDPI, Color.black);
+
+        // end points
+        buf.drawEllipseF(points[0].x, points[0].y, 5,5, 1, Color.antique_white, Color.cyan);
+        buf.drawEllipseF(points[2].x, points[2].y, 5,5, 1, Color.antique_white, Color.cyan);
+        buf.drawEllipseF(points[1].x, points[1].y, 3,3, 0, Color.antique_white, Color.cyan);
+
+        // draw the direction & normal vectors
+        auto segStep = 1f/segmentCount;
+        foreach(i; 0..segmentCount) {
+            auto dir = bezierQuadraticDirection(points, i*segStep);
+            auto norm = dir.rotated90ccw;
+            auto point = lines[i];
+            buf.drawLineF(point, point + (dir * 15f), 3.scaledByDPI, Color.yellow );
+            buf.drawLineF(point, point + (norm * 15f), 3.scaledByDPI, Color.red );
+    }
+
+        drawText(buf,rc, sampleName());
+    }
+}
+
+
+
+void drawCubicControlsGuides(DrawBuf buf, vec2[] controls) {
+    buf.drawLineF(controls[0], controls[1], 1, Color.black);
+    buf.drawLineF(controls[2], controls[3], 1, Color.black);
+    buf.drawEllipseF(controls[0].x, controls[0].y, 5,5, 1, Color.antique_white, Color.cyan);
+    buf.drawEllipseF(controls[3].x, controls[3].y, 5,5, 1, Color.antique_white, Color.cyan);
+    buf.drawEllipseF(controls[1].x, controls[1].y, 3,3, 0, Color.antique_white, Color.cyan);
+    buf.drawEllipseF(controls[2].x, controls[2].y, 3,3, 0, Color.antique_white, Color.cyan);
+}
+
+void drawCubicSegmentsNormDir(DrawBuf buf, vec2[] controls, int segmentCount, vec2[] segments, bool direction, bool normals) {
+    if ( !direction && !normals && segments.length < 2)
+        return;
+    // draw the direction & normal vectors
+    auto segStep = 1f/segmentCount;
+    foreach(i; 0..segmentCount) {
+        auto dir = bezierCubicDirection(controls, i*segStep);
+        auto norm = dir.rotated90ccw;
+        auto point = segments[i];
+        if ( direction )
+        buf.drawLineF(point, point + (dir * 15f), 3.scaledByDPI, Color.yellow );
+        if ( normals )
+        buf.drawLineF(point, point + (norm * 15f), 3.scaledByDPI, Color.red );
+    }
+}

src/dlangui/core/math3d.d

@@ -1740,3 +1740,143 @@ vec3 triangleNormal(float[3] p1, float[3] p2, float[3] p3) {
 
 /// Alias for 2d float point
 alias PointF = vec2;
+
+
+
+
+// this form can be used within shaders
+/// cubic bezier curve
+PointF bezierCubic(const PointF[] cp, float t) pure @nogc @safe
+    in { assert(cp.length > 3); } do
+{
+    // control points
+    auto p0 = cp[0];
+    auto p1 = cp[1];
+    auto p2 = cp[2];
+    auto p3 = cp[3];
+
+    float u1 = (1.0 - t);
+    float u2 = t * t;
+    // the polynomials
+    float b3 = u2 * t;
+    float b2 = 3.0 * u2 * u1;
+    float b1 = 3.0 * t * u1 * u1;
+    float b0 = u1 * u1 * u1;
+    // cubic bezier interpolation
+    PointF p = p0 * b0 + p1 * b1 + p2 * b2 + p3 * b3;
+    return p;
+}
+
+/// quadratic bezier curve (not tested)
+PointF bezierQuadratic(const PointF[] cp, float t) pure @nogc @safe
+    in { assert(cp.length > 2); } do
+{
+    auto p0 = cp[0];
+    auto p1 = cp[1];
+    auto p2 = cp[2];
+
+    float u1 = (1.0 - t);
+    float u2 = u1 * u1;
+
+    float b2 = t * t;
+    float b1 = 2.0 * u1 * t;
+    float b0 = u2;
+
+    PointF p = p0 * b0 + p1 * b1 + p2 * b2;
+    return p;
+}
+
+/// cubic bezier (first) derivative
+PointF bezierCubicDerivative(const PointF[] cp, float t) pure @nogc @safe 
+    in { assert(cp.length > 3); } do 
+{
+    auto p0 = cp[0];
+    auto p1 = cp[1];
+    auto p2 = cp[2];
+    auto p3 = cp[3];
+
+    float u1 = (1.0 - t);
+    float u2 = t * t;
+    float u3 = 6*(u1)*t;
+    float d0 = 3 * u1 * u1;
+    // -3*P0*(1-t)^2 + P1*(3*(1-t)^2 - 6*(1-t)*t) + P2*(6*(1-t)*t - 3*t^2) + 3*P3*t^2
+    PointF d = p0*(-d0) + p1*(d0 - u3) + p2*(u3 - 3*u2) + (p3*3)*u2;
+    return d;
+}
+
+/// quadratic bezier (first) derivative
+PointF bezierQuadraticDerivative(const PointF[] cp, float t) pure @nogc @safe 
+    in { assert(cp.length > 2); } do 
+{
+    auto p0 = cp[0];
+    auto p1 = cp[1];
+    auto p2 = cp[2];
+
+    float u1 = (1.0 - t);
+    // -2*(1-t)*(p1-p0) + 2*t*(p2-p1);
+    PointF d = (p0-p1)*-2*u1 + (p2-p1)*2*t;
+    return d;
+}
+
+// can't be pure due to normalize & vec2 ctor
+/// evaluates cubic bezier direction(tangent) at point t
+PointF bezierCubicDirection(const PointF[] cp, float t) {
+    auto d = bezierCubicDerivative(cp,t);
+    d.normalize();
+    return PointF(tan(d.x), tan(d.y));
+}
+
+/// evaluates quadratic bezier direction(tangent) at point t
+PointF bezierQuadraticDirection(const PointF[] cp, float t) {
+    auto d = bezierQuadraticDerivative(cp,t);
+    d.normalize();
+    return PointF(tan(d.x), tan(d.y));
+}
+
+/// templated version of bezier flatten curve function, allocates temporary buffer
+PointF[] flattenBezier(alias BezierFunc)(const PointF[] cp, int segmentCountInclusive) 
+    if (is(typeof(BezierFunc)==function)) 
+{
+    if (segmentCountInclusive < 2)
+        return PointF[].init;
+    PointF[] coords = new PointF[segmentCountInclusive+1];
+    flattenBezier!BezierFunc(cp, segmentCountInclusive, coords);
+    return coords;
+}
+
+/// flatten bezier curve function, writes to provided buffer instead of allocation
+void flattenBezier(alias BezierFunc)(const PointF[] cp, int segmentCountInclusive, PointF[] outSegments)
+    if (is(typeof(BezierFunc)==function)) 
+{
+    if (segmentCountInclusive < 2)
+        return;
+    float step = 1f/segmentCountInclusive;
+    outSegments[0] = BezierFunc(cp, 0);
+    foreach(i; 1..segmentCountInclusive) {
+        outSegments[i] = BezierFunc(cp, i*step);
+    }
+    outSegments[segmentCountInclusive] = BezierFunc(cp, 1f);
+}
+
+
+/// flattens cubic bezier curve, returns PointF[segmentCount+1] array or empty array if <1 segments
+PointF[] flattenBezierCubic(const PointF[] cp, int segmentCount) {
+    return flattenBezier!bezierCubic(cp,segmentCount);
+}
+
+/// flattens quadratic bezier curve, returns PointF[segmentCount+1] array or empty array if <1 segments
+PointF[] flattenBezierQuadratic(const PointF[] cp, int segmentCount) {
+    return flattenBezier!bezierQuadratic(cp, segmentCount);
+}
+
+/// calculates normal vector at point t using direction
+PointF bezierCubicNormal(const PointF[] cp, float t) {
+    auto d = bezierCubicDirection(cp, t);
+    return d.rotated90ccw;
+}
+
+/// calculates normal vector at point t using direction
+PointF bezierQuadraticNormal(const PointF[] cp, float t) {
+    auto d = bezierQuadraticDerivative(cp, t);
+    return d.rotated90ccw;
+}