Smooth Parametric Bezier Curve in a Script Panel

sinewavekid

smooth bezier spline

hi magical HISE friends! here's the code i got so far for this smooth parametric bezier curve in a script panel. i currently don't have a use for it (yet) but wanted to share it because it seems useful, especially with a few custom tweaks

the main features:

parametric

adjustable amount of equally spaced points/circles (locked in their x positions)
the points and line are always centered to your script panel resolution
the padding between the panel's width and height is easily adjustable (as a ratio rather than pixel values) (the padding border is drawn as the inset rectangle)

super smooth bezier path, different than "quadraticTo" . based on the code i found here

Smooth Bézier Spline Through Prescribed Points

double click to reset values to starting position (.5 in this case)
save in preset works for me (each point automatically links to hidden sliders in this example)

hise snippet

HiseSnippet 3684.3oc6aztaabb7niYZrZcaBPe.15BjbLhhhTVJI0Ltw1z1oFN1Vvzw0DBBAKuaI4Ve7tC2GRjwP+ouM8sn.8EoOB8e8msyreb2tGORKo3XfBTAaQt6NyryNesyN6pCSh7XooQINMt1KVFybZ7qZNbYX1rAyn7PmGcemF+9lCmGEkMibHMgNmkkv8H2i8ibVBYPdxILxI8bt2xXZZJy2oQiO3aQDabsq5H94e8M2iFPC8Xkc437xHtG663y4Yk8d3cdLOH3gTe1K3yMfd+67HunvAQAQ4.S9AM65DS8dMcJ6oTDrqzzowG9.edVTxvLZFKEf4dQ9KGNK5zPI7ujmxGGvvF8bFBDR1syfY7.+C0BfTGmFW8vRwwGHEG+1lOg6yK5uTr7whAHkXXJCZbkMwR8t.rTCCV5pRV5SZNzKgGmUNBxO+xlOJLikLgBhZSVQBqyU92eVyAQ.DgYclSeM6gIPiBLb+htcaStY2ts5e8st9V6tqFTpuOvq4zfuMm6ybOBfp2AcOtMo6h8u6CE+fnrdDtIR3UQ35aAJ0zLxIzDvtJjEzibahlFSYYChlGGEBMbugb3aHwBgOLe9.dhW.KEv4K5SH6tKYTTNwiFR7lQCmxHYy3oHbiAizrHBOzKgQSYjnDhOS88rYLMHQSHdRJJmgAITedNR9d6CzWLCOW1E.JhnE3or.lWFOJ74ZzzD3yI857U8MYPp+eIGV2HMlmGjwiCPGIJvsLlOyWuF4ggrD4pTRzGR8.6Ifzc6z6OHnnpGX44y.03bdnbMkx+QllMEjwlY8SnSmxCm9nPe1Bfd6zSPsWDQxR.GKxoy3dyTnP.o3XF.rDKI6Up3dB3KbHnvA.dEJqNPPoTv+DQYLK6TFKjDi5Oxob+rY8I85h.tK7Avgh9VCAGgv0cCDbFiOcVFo2dFDT1mVFZvZlbpfl97S.WvnPxDoTbB7+WATV.hE5irQezZQeTI5JqnKJCnspqvHCtnbhlNVbD.6iB4YbZ.ZeHrgA2sjn.PxGjCPSSRnKM0Fpweob3aSN5XvEDouqvBEsE6Ce70FNjP6s2tE4MWeKzqwh.chySm4ZDl3wgQicugIL+vMHaS3PnB3esP+8UHxQ7i6jxffBmHCfdi1v5NHksIfeNFQvsaGLzE9K3a81Lw8YSnfuon2afHbvlgOkdB6QgGlvfV.7YI4ajgDMbUT8Lkt4twwAKIoABiZP9xoX.kTz8VDqfGxmmOmPC8IyoKDeejRyYpy.3d1jIvjHhTzsa2dx3iOQgejXPKLnKrwXOEFpYQiAn5yCEQ4HTjWG8xBlzUvGsgnMPHkBsOR7hEBP7RVaahq.TH7na4zuSIDsH6RbMByuCoWg8.RVYPTlOrp.BWLI0AAEiw0CnfITR3Jj5kbYTHzTIxmvS.QjLPnDA9DMie6aCBqhUpbRAQ.Yayk4tj8DtnCeM6TCJJgTpoCVJovYZdJgkkmDBB+rYv1zKbkegGpEwFqqVsMkCl1ROTqnvs9lGGvlCtbBN3EyhlC60PClFkvylMWDtHMJ3DL9JjYmOmNMJjFPRWBzcdpgROSfpKsMYbahWahukhF0CzNArvoPT9xt8hkwMPwfGINAxrqbPeiA8qN3B0XhM.hBxQdPKjpMFDZjXG9oPkUi5R3aFKiI4A9kfxZL7g1HS+iuBD+5A4LBCB97VnqKhEvcT7iOGF8HNxqG2ZcSlb1JPvu.gyKwNqvnB+XwOIphxeo.THgsTAn3G6cOTE7Gkphc1wRNu.o3sEyFNAdwxY.5FhBz6390a9uvvXdHjgDjYyDCaZOZfWd.jYcwVXwQ7vrTAWI1YKeLdHk+weSbJEO7TJFVxdPtk4YrARbOTfp6isLmi6o2uqnm8p1CZx+XkIuv3SNTQrkmiN36LCiXmBoBSNggaPmZDiRPQveR8om5yD8LUPpuiMIam4QPviT1TzYVNB8ntGK7.jMGKatmdqGYSMekHa9X7isI6AJgGeTOqYQbZ.gyubRRqwaq2F81nRscOCawwxt12nKuUgJQAkfq3kLX8VIEB25DIBVyTNLtrqurPzTzU2BwSQWekXpUM2F+pkXBNtFbn26t31iI4oXbypAU2fXaUQlXKXL3YQDFw7tpDT4hNG8OWEHk.LoDnDafJDdw8JWoEK5cKjR8qg6q3iuyNbqk.PQwj6plcOoON1sP80RE4rF03.oqH5coyk4BFfOdO4jaZu.PVL48shEBPWp46b.l.BpdAHKDKs5WIXzafwtE7+1.12B4zyVyVs34Jg0BkjJqWRLr2MbFG3W0DOBxraFMifmSG9VRT9zYDFs3jWeVJwig9ilwsDzWVLlCAZ6F2VE3qPh.bzCVfmiKCNDAF4ANBPTJWlJYJKll.TPmzgXaVY3OPbHoDjzQrqdFciABqECwcVzmblYVXKu.3tTgaoleSwvWH3cC1zyLVMddpZigqVLl7nEhiVGhKKQrLlaTTrslQEnQvav4gk4zgJYksUmzLZR1SYmNLerP+n3mivxerr36s5udibkfzXSkZCX3E2SJDLkJcD9g8WAxQUgbzZfbu5n4d0BYczrFHYg9hgQBqEFVtkUADo6xp.VBJnVtuVvWiOkZ+edp8dBRki.9WD4dDJ7ZKDLfZ4HbY2VrjfVE7a4WG0pLBhvoWVNJ7bbGBmEO64QPpogrR69oEZqoclvCBtaPfqr5kocFGP8dskU12xxTlQXMMvR2XjxA12eFqQBHUvkEVXLQaWSSbAX+IY0PJgS1g6Z74T0EfLllx7Ihr6YUKkPp4TTTHCClZ2xJbzeEXGogUwYk.OpdVB4frnLH8CeN3HE5gMIiw3CmvR.tb7RY4sTUCxksvKHWrJvtwBtwEtl50FUJYAEYZqR1SLECUzvZ4rCwE2DQuVao6PUKuVqmsqVfJg4oH58p0KTyGCRK3AKVZ0C9ZcdUrFMnbIETPLqn6ns+JyhriQGV.U0LKsWHlzylwKsTpT0Hw9ak0qXC6eulhDU8D6hpifIDUsHCqTJko5Ro.mDl2pRDkAREfzLTYQtcQcY2l35ZZctCwP0OR0Tq3guZwblSUUArpJWpIuUMo7TQEVJiMj8tpMuaUUSthh7xJsUb3qJEOuxV7vQAfxFcCx1pqe68.pvzRgyaHKtUw7CaLdqR5cVcBrgpPjdPPzjhi3Utu6TLVrLBaQf1krffnSml.di19s5TzBYmJyOCky.OhFfgKIwIrS3QfDvSVmRivZF2OgLQLwV7ZFF1eAIhacylHDgHqMlubRkmantrBUmOolL8pHKsln6uZ1HS6fonTjlH5rbunbHVnaOvcoW8nqb1aqhdArqv8VGQcRRzbicqX9SYWRGdic9pX7WNIp5QuFq1JhCLdvh2lYpEzKWalEmNiCZsTHXyqwPd4YXAHJA8bXuUBJpDdPP.ONk4dTA6ui1SqcISZ1WwsGsmUiisTbUY6z4zf.lnbdbe0hPeMNgXEHrkNxaXJY0arZMW8j0xBSrotkkIQsVa1CXM2hUY0dNttHA1aVMVXNWDPHg4AYMLMvHAJrKyHb8sGxbuAYgZw72sIVo4XFbbfhqSwjL5LzrRkvLShJSaQpZqeCH4MxYwGPnX71.vpHmGTb6Wn6IOTu2c4k8T0Ns6hCdP4kuV0xobVnInP0LVvmIkyL7nj31AZqHoo8yALcORHmaKkosKkIsMVt3E.2YeQQp0WwL4t99j4PvVFVPufw3kOBaKNGR2qHqCHyuLNN5RyDueBhz.ENkYdyNAL2rKimYFzJ7OG4PWBoQVz+rkKbMYD5dARKs0lRYDK+sPrzwOJeb.aP.GN.RkHwClw.QOWlumDtc7P.wq+0vBCulY0E.A6OgIHhaYZdAIWlsB9ImQxOOY7sgrMsCAqEyhapgNNUIuWfAzUKoVju91q7HA9zOkTAkkknLpNTVQroqEJduipX.VYmqygWRGvEVscf5BtTWyIQbUjqR425UWVEAkaSBKFOXrq7tCdNynTIXVCvjmG6qChWTsK89+qRVYMj5KqsEOiPm.BHh3xVyDm9KhPOIB1xaRdBPRHQNOYJxByVvDVGcwlzmU28kT0qQ3Fv72nGy+2U4+QbUp9xW3Fa5qGSYwTQQUTJdPY959WH6H6I82gu2lpVSeeo6v42AdRDlwo7sAfaGZmbGb7F84nW8pjMjgFJ0BE5tjyu1GSHEerFlm4yxZvZ4aDBQyflX9NL9QMtxBoz2GaI7WyagZHlqWgEwoyTkzQlqBXdj.pCrbHkEFrU+hpzGE9znL1yBcas0a15Zac1VjpCMYRsioJIMjBesCiuJxjMgnq7wr0VZ5T.nSiqZ+VD+vy2aQTcBXC.iBwGPzyhYp1OLJvGeig32W8kK5nNsrCLiJND.MS7BF+0pWv3P3jJrDGtO9bJsdIPccDqhxmA5+7abt3To26Dpr26Dpby2ITY+2IT4fZnx2+n6Syn3KNUo3.kYLl9MZyz39rS3dL46O8ZMuOK80fOhSieQw6zD5VN6WW+5TQuUwj+QMkd1NKbZzrANcK0eQ7B.KXi+9e8Nxy0T1SxcFGk.qBYXcy2Prr+g7ez5kESwnh5iF.v+aZdW3zRkc3Xvve342XbUN+DsWiro4SFqhx4hOe8dOOe68dd9t4644a+2yy2A+DluUet2ebymD4ik8v90miOyd0.v1.VO4a7gbDBaGtz7Y3eAdR5c23SR+7xheRyC4YdypmGuRM7HD64mCdT8P9udyGLYBjEUICd0lO7UW1Ws+aY5k2J3THkqDNZK7z74CixS7XvrGBwBSQ6fqfaRJa2UaWLjE5KZ7efeTC1Ca2PMXO8fNyodIQ+fxvC+SE3iD8.7Tn3uLhq07IXaxJaB53Lm6y+AOOaRsBh6cYQ7lWVD2+xh3AWVD+hKKhe4kEwu5siH9GVxcyyhlKcabbdxgOPr4biFOHjBVfBqUm+KfEn2uX

the code

Content.makeFrontInterface(600, 300);

//Content.addVisualGuide([0, 150], 0x4AFFFFFF);
//Content.addVisualGuide([300, 0], 0x4AFFFFFF);

const var Panel1 = Content.getComponent("Panel1");

var numCircles = 6;  // You can change this number to increase or decrease the number of circles
var Cradius = 14;    // Radius of the circles
var selectionRadius = Cradius * 1.8; // You can adjust the multiplier as needed

var innerCircleRadiusFactor = 0.19; // Factor to determine the size of the inner circles
var draggingIndex = -1; // To track which circle is being dragged

const var MainPaddingX = 15; // spacing between panel width; 10 = 1/10 of width
const var MainPaddingY = 10; // spacing between panel height 12 = 1/10 of height

var PaddingX = MainPaddingX; // division factor for X padding
var PaddingY = MainPaddingY; // division factor for Y padding

var CPaddingX = MainPaddingX; // division factor for Circles X padding
var CPaddingY = MainPaddingY; // division factor for Circles Y padding

// Initialize the control values array
const var controlValues = [];
for (var i = 0; i < numCircles; i++) {
    controlValues.push(Content.addKnob("controlValue_" + i, 0, 0));
    controlValues[i].set("visible", false);
    controlValues[i].setRange(0.0, 1.0, 0.01);
    controlValues[i].set("defaultValue", 0.5);
    controlValues[i].set("saveInPreset", true);
    controlValues[i].setValue(0.5);
}

// Apply slight variations to the minimum and maximum Y values
const var minOffset = 0.0001;  // Minimum offset
const var maxOffset = 0.0002;  // Maximum offset

function applyYVariations(value, index) {
    var variation = minOffset + (index * (maxOffset - minOffset) / (numCircles - 1));
    var adjustedMin = variation;
    var adjustedMax = 1 - variation;

    // Apply variation only to the first circle
    if (index === 0) {
        value += minOffset / 2; // Skew the first value slightly
    }

    return Math.max(Math.min(value, adjustedMax), adjustedMin);
}

// Function to implement the Thomas algorithm for solving tridiagonal systems
function thomas(a, b, c, d) {
    var n = a.length;
    var cp = []; // c prime
    var dp = []; // d prime
    var x = [];  // solution

    for (var i = 0; i < n - 1; i++) {
        if (i === 0) {
            cp.push(c[i] / b[i]);
            dp.push(d[i] / b[i]);
        } else {
            cp.push(c[i] / (b[i] - a[i] * cp[i - 1]));
            dp.push((d[i] - a[i] * dp[i - 1]) / (b[i] - a[i] * cp[i - 1]));
        }
    }
    x.push((d[i] - a[i] * dp[i - 1]) / (b[i] - a[i] * cp[i - 1])); // i === n - 1

    for (i = n - 2; i >= 0; i--) {
        x[i] = dp[i] - cp[i] * x[i + 1];
    }

    return x;
}

// Spline function to calculate control points for the cubic Bézier curve
function computeControlPoints(K) {
    var p1 = [];
    var p2 = [];
    var n = K.length - 1;
    
    // Right-hand side vectors
    var a = [], b = [], c = [], r = [];

    // Left-most segment
    a[0] = 0;
    b[0] = 2;
    c[0] = 1;
    r[0] = K[0] + 2 * K[1];

    // Internal segments
    for (var i = 1; i < n - 1; i++) {
        a[i] = 1;
        b[i] = 4;
        c[i] = 1;
        r[i] = 4 * K[i] + 2 * K[i + 1];
    }

    // Right-most segment
    a[n - 1] = 2;
    b[n - 1] = 7;
    c[n - 1] = 0;
    r[n - 1] = 8 * K[n - 1] + K[n];

    // Solve Ax=b using Thomas algorithm
    for (var i = 1; i < n; i++) {
        var m = a[i] / b[i - 1];
        b[i] = b[i] - m * c[i - 1];
        r[i] = r[i] - m * r[i - 1];
    }

    p1[n - 1] = r[n - 1] / b[n - 1];
    for (var i = n - 2; i >= 0; --i) {
        p1[i] = (r[i] - c[i] * p1[i + 1]) / b[i];
    }

    // Compute p2 values
    for (var i = 0; i < n - 1; i++) {
        p2[i] = 2 * K[i + 1] - p1[i + 1];
    }
    p2[n - 1] = 0.5 * (K[n] + p1[n - 1]);

    return { p1: p1, p2: p2 };
}

// Function to create a smooth path with cubic Bézier curves that pass through each circle's center
function createSmoothPath(p, points) {
    // Extract X and Y positions separately
    var xPoints = points.map(function(p) { return p.x; });
    var yPoints = points.map(function(p) { return p.y; });

    // Calculate control points for x and y
    var controlPointsX = computeControlPoints(xPoints);
    var controlPointsY = computeControlPoints(yPoints);

    // Loop through each segment and draw the path
    p.startNewSubPath(xPoints[0], yPoints[0]);
    for (var i = 0; i < points.length - 1; i++) {
        var cp1X = controlPointsX.p1[i];
        var cp1Y = controlPointsY.p1[i];
        var cp2X = controlPointsX.p2[i];
        var cp2Y = controlPointsY.p2[i];
        var endPointX = xPoints[i + 1];
        var endPointY = yPoints[i + 1];

        // Draw the cubic Bézier curve for this segment
        p.cubicTo([cp1X, cp1Y], [cp2X, cp2Y], endPointX, endPointY);
    }
}

Panel1.setPaintRoutine(function(g) {
    g.fillAll(Colours.black);

    // Get the panel size
    var panelWidth = this.getWidth();
    var panelHeight = this.getHeight();

    // Calculate padding based on the division factors
    var paddingX = panelWidth / CPaddingX;
    var paddingY = panelHeight / CPaddingY;

    // Calculate the total distance to be covered by the spacing (excluding the radii and padding at the ends)
    var totalSpacing = panelWidth - (2 * paddingX) - (2 * Cradius);

    // Calculate the spacing between the centers of the circles
    var Cspacing = totalSpacing / (numCircles - 1);

    // Array to store Y positions for circles
    var circleYPositions = [];

    // Calculate the Y positions of the circles based on control values with variations
    for (var i = 0; i < numCircles; i++) {
        var adjustedValue = applyYVariations(controlValues[i].getValue(), i);
        var CcenterY = paddingY + Cradius + ((panelHeight - 2 * paddingY - 2 * Cradius) * adjustedValue);
        circleYPositions.push(CcenterY);
    }

    // Array to store the circle positions (X and Y)
    var circlePositions = [];
    for (var i = 0; i < numCircles; i++) {
        var CcenterX = paddingX + Cradius + (i * Cspacing);
        var CcenterY = circleYPositions[i];
        circlePositions.push({ x: CcenterX, y: CcenterY });
    }

    // Set the color for the path
    g.setColour(Colours.yellowgreen);

    // Create a new path and clear any previous content
    var p = Content.createPath();
    p.clear();

    // Create the smoothed path using cubic Bézier curves
    createSmoothPath(p, circlePositions);

    // Draw the path
    g.drawPath(p, p.getBounds(1), 1);

    // Draw the circles, centered with padding from the panel edges
    for (var i = 0; i < numCircles; i++) {
        // Get the circle position from the array
        var CcenterX = circlePositions[i].x;
        var CcenterY = circlePositions[i].y;

        // Draw the white stroked outline
        g.setColour(Colours.yellowgreen);
        g.drawEllipse([CcenterX - Cradius, CcenterY - Cradius, Cradius * 2, Cradius * 2], 1);

        // Draw the smaller solid white circle inside
        var innerCradius = Cradius * innerCircleRadiusFactor;
        g.fillEllipse([CcenterX - innerCradius, CcenterY - innerCradius, innerCradius * 2, innerCradius * 2]);
    }

    // Calculate the bounds for the rectangle
    var rectX = paddingX;
    var rectY = paddingY; // Start the rectangle from the top padding
    var rectWidth = panelWidth - 2 * paddingX;
    var rectHeight = panelHeight - 2 * paddingY; // The rectangle spans the full height within the Y padding

    g.setColour(0x5EFFFFFF);
    // Draw the rectangle around the circles' bounded Y space
     g.drawRect([rectX, rectY, rectWidth, rectHeight], 0.4);
});

// Add mouse callback to move circles vertically
Panel1.setMouseCallback(function(event) {
    var panelWidth = Panel1.getWidth();
    var panelHeight = Panel1.getHeight();
    var paddingX = panelWidth / CPaddingX;
    var paddingY = panelHeight / CPaddingY;
    var Cspacing = (panelWidth - (2 * paddingX) - (2 * Cradius)) / (numCircles - 1);

    if (event.doubleClick) {
        // Check if the double-click is within the detection area of any circle
        for (var i = 0; i < numCircles; i++) {
            var CcenterX = paddingX + Cradius + (i * Cspacing);
            var CcenterY = paddingY + Cradius + ((panelHeight - 2 * paddingY - 2 * Cradius) * controlValues[i].getValue());

            if (Math.abs(event.x - CcenterX) <= selectionRadius && Math.abs(event.y - CcenterY) <= selectionRadius) {
                // Reset the Y control value of the selected circle to the default (0.5)
                controlValues[i].setValue(0.5);
                Panel1.repaint(); // Redraw the panel to update the circle's position
                return; // Exit after resetting to avoid further actions in this callback
            }
        }
    }

    if (event.clicked) {
        // Check if the click is within the detection area of any circle
        for (var i = 0; i < numCircles; i++) {
            var CcenterX = paddingX + Cradius + (i * Cspacing);
            var CcenterY = paddingY + Cradius + ((panelHeight - 2 * paddingY - 2 * Cradius) * controlValues[i].getValue());

            if (Math.abs(event.x - CcenterX) <= selectionRadius && Math.abs(event.y - CcenterY) <= selectionRadius) {
                draggingIndex = i; // Start dragging this circle
                break;
            }
        }
    }

    if (draggingIndex != -1) {
        // Update the Y control value of the selected circle to follow the mouse
        var newValue = Math.max(Math.min((event.y - paddingY - Cradius) / (panelHeight - 2 * paddingY - 2 * Cradius), 1), 0);
        controlValues[draggingIndex].setValue(newValue);
        Panel1.repaint(); // Redraw the panel to update the circle's position
    }

    if (event.mouseUp) {
        draggingIndex = -1; // Stop dragging when the mouse is released
    }
});

i have been messing about with more interactive / animated hise panels, and collaborating with chatGPT , so please let me know if this code works for you and if have any suggestions to make this code even better or simpler please share it !

d.healey

@sinewavekid The code needs a bit of work to correct ChatGPT's output but the end result looks very nice!

Mighty23

WOW! this looks amazing.

Smooth Parametric Bezier Curve in a Script Panel

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