Face Hexagons Grid
Learn how to create hexagonal face patterns that respond to a control point. Hexagons closer to the control point become larger, while distant ones become smaller, creating organic wave-like effects.
Key Concepts
- Control Point: A point that influences the hexagon sizes based on distance
- Distance Scaling: Hexagons scale up/down based on how far they are from the control point
- UV Coordinates: Position the control point using 0-1 values instead of exact coordinates
- Pattern Filtering: Selectively remove some hexagons to create openings
- Rete
- Blockly
- TypeScript
Script Source (rete)
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Script Source (blockly)
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type="bitbybit.point.distancesToPoints" id="distancesToPoints"><value name="StartPoint"><block type="variables_get" id="getControlPointForDistances"><field name="VAR" id="controlPoint">controlPoint</field></block></value><value name="EndPoints"><block type="variables_get" id="getHexCentersForDistances"><field name="VAR" id="hexCenters">hexCenters</field></block></value></block></value><next><block type="variables_set" id="setMinDistance"><field name="VAR" id="minDistance">minDistance</field><value name="VALUE"><block type="bitbybit.vector.min" id="vectorMin"><value name="Vector"><block type="variables_get" id="getDistancesForMin"><field name="VAR" id="distances">distances</field></block></value></block></value><next><block type="variables_set" id="setMaxDistance"><field name="VAR" id="maxDistance">maxDistance</field><value name="VALUE"><block type="bitbybit.vector.max" id="vectorMax"><value name="Vector"><block type="variables_get" id="getDistancesForMax"><field name="VAR" id="distances">distances</field></block></value></block></value><next><block type="variables_set" id="setScalePattern"><field name="VAR" id="scalePattern">scalePattern</field><value name="VALUE"><block type="lists_create_with" id="emptyScalePattern"><mutation items="0"></mutation></block></value><next><block type="controls_forEach" id="forEachDistance"><field name="VAR" id="distance">distance</field><value name="LIST"><block type="variables_get" id="getDistancesForLoop"><field name="VAR" id="distances">distances</field></block></value><statement name="DO"><block type="variables_set" id="setScaledValue"><field name="VAR" id="scaledValue">scaledValue</field><value name="VALUE"><block type="bitbybit.math.remap" id="remapDistance"><value name="Number"><block type="variables_get" id="getCurrentDistance"><field name="VAR" id="distance">distance</field></block></value><value name="FromLow"><block type="variables_get" id="getMinDistance"><field name="VAR" id="minDistance">minDistance</field></block></value><value name="FromHigh"><block type="variables_get" id="getMaxDistance"><field name="VAR" id="maxDistance">maxDistance</field></block></value><value name="ToLow"><block type="math_number" id="toLowValue"><field name="NUM">0.211</field></block></value><value name="ToHigh"><block type="math_number" id="toHighValue"><field name="NUM">0.9</field></block></value></block></value><next><block type="lists_setIndex" id="addScaledValue"><mutation at="false"></mutation><field name="MODE">INSERT</field><field name="WHERE">LAST</field><value name="LIST"><block type="variables_get" id="getScalePatternList"><field name="VAR" id="scalePattern">scalePattern</field></block></value><value name="TO"><block type="variables_get" id="getScaledValue"><field name="VAR" id="scaledValue">scaledValue</field></block></value></block></next></block></statement><next><block type="variables_set" id="setInclusionPattern"><field name="VAR" id="inclusionPattern">inclusionPattern</field><value name="VALUE"><block type="bitbybit.json.parse" id="parseInclusionPattern"><value name="Text"><block type="text" id="inclusionPatternText"><field name="TEXT">[true, true, true, true, false]</field></block></value></block></value><next><block type="variables_set" id="setHexagonFaces"><field name="VAR" id="hexagonFaces">hexagonFaces</field><value name="VALUE"><block type="base_time_await_return" id="awaitHexagonFaces"><value name="Promise"><block type="bitbybit.occt.shapes.face.hexagonsInGrid" id="hexagonsInGrid"><value name="Width"><block type="variables_get" id="getWidthForHexFaces"><field name="VAR" id="gridWidth">gridWidth</field></block></value><value name="Height"><block type="variables_get" id="getHeightForHexFaces"><field name="VAR" id="gridHeight">gridHeight</field></block></value><value name="NrHexagonsInWidth"><block type="variables_get" id="getHexWidthForFaces"><field name="VAR" id="hexagonsInWidth">hexagonsInWidth</field></block></value><value name="NrHexagonsInHeight"><block type="variables_get" id="getHexHeightForFaces"><field name="VAR" id="hexagonsInHeight">hexagonsInHeight</field></block></value><value name="FlatTop"><block type="logic_boolean" id="flatTopForFaces"><field name="BOOL">TRUE</field></block></value><value name="ExtendTop"><block type="logic_boolean" id="extendTopForFaces"><field name="BOOL">FALSE</field></block></value><value name="ExtendBottom"><block type="logic_boolean" id="extendBottomForFaces"><field name="BOOL">FALSE</field></block></value><value name="ExtendLeft"><block type="logic_boolean" id="extendLeftForFaces"><field name="BOOL">FALSE</field></block></value><value name="ExtendRight"><block type="logic_boolean" id="extendRightForFaces"><field name="BOOL">FALSE</field></block></value><value name="ScalePatternWidth"><block type="variables_get" id="getScalePatternForWidth"><field name="VAR" id="scalePattern">scalePattern</field></block></value><value name="ScalePatternHeight"><block type="variables_get" id="getScalePatternForHeight"><field name="VAR" id="scalePattern">scalePattern</field></block></value><value name="InclusionPattern"><block type="variables_get" id="getInclusionPattern"><field name="VAR" id="inclusionPattern">inclusionPattern</field></block></value></block></value></block></value><next><block type="variables_set" id="setAffectorPoint"><field name="VAR" id="affectorPoint">affectorPoint</field><value name="VALUE"><block type="bitbybit.vector.add" id="addAffectorOffset"><value name="First"><block type="variables_get" id="getControlPointForAffector"><field name="VAR" id="controlPoint">controlPoint</field></block></value><value name="Second"><block type="bitbybit.vector.vectorXYZ" id="affectorOffset"><value name="X"><block type="math_number" id="affectorOffsetX"><field name="NUM">0</field></block></value><value name="Y"><block type="math_number" id="affectorOffsetY"><field name="NUM">3</field></block></value><value name="Z"><block type="math_number" id="affectorOffsetZ"><field name="NUM">0</field></block></value></block></value></block></value><next><block type="variables_set" id="setPin"><field name="VAR" id="pin">pin</field><value name="VALUE"><block type="base_time_await_return" id="awaitPin"><value name="Promise"><block type="bitbybit.occt.dimensions.pinWithLabel" id="pinWithLabel"><value name="StartPoint"><block type="variables_get" id="getControlPointForPin"><field name="VAR" id="controlPoint">controlPoint</field></block></value><value name="EndPoint"><block type="variables_get" id="getAffectorPointForPin"><field name="VAR" id="affectorPoint">affectorPoint</field></block></value><value name="Direction"><block type="bitbybit.vector.vectorXYZ" id="pinDirection"><value name="X"><block type="math_number" id="pinDirectionX"><field name="NUM">0</field></block></value><value name="Y"><block type="math_number" id="pinDirectionY"><field name="NUM">0</field></block></value><value name="Z"><block type="math_number" id="pinDirectionZ"><field name="NUM">1</field></block></value></block></value><value name="OffsetFromStart"><block type="math_number" id="pinOffset"><field name="NUM">0.1</field></block></value><value name="Label"><block type="text" id="pinLabel"><field name="TEXT">Affector</field></block></value><value name="LabelOffset"><block type="math_number" id="pinLabelOffset"><field name="NUM">0.3</field></block></value><value name="LabelSize"><block type="math_number" id="pinLabelSize"><field name="NUM">0.1</field></block></value></block></value></block></value><next><block type="bitbybit.draw.drawAnyAsyncNoReturn" id="drawHexagonFaces"><value name="Entity"><block type="variables_get" id="getHexagonFacesForDraw"><field name="VAR" id="hexagonFaces">hexagonFaces</field></block></value><next><block type="bitbybit.draw.drawAnyAsyncNoReturn" id="drawPin"><value name="Entity"><block type="variables_get" id="getPinForDraw"><field name="VAR" id="pin">pin</field></block></value><next><block type="bitbybit.draw.drawAnyAsyncNoReturn" id="drawControlPoint"><value name="Entity"><block type="variables_get" id="getControlPointForDraw"><field name="VAR" id="controlPoint">controlPoint</field></block></value></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></next></block></xml>
Script Source (typescript)
// Import required DTOs and types for face hexagon grid creation
const { HexagonsInGridDto, RectangleDto, DataOnUVDto, PinWithLabelDto } = Bit.Inputs.OCCT;
const { HexGridScaledToFitDto } = Bit.Inputs.Point;
const { RemapNumberDto } = Bit.Inputs.Math;
const { HexGridData } = Bit.Models.Point;
type Point3 = Bit.Inputs.Base.Point3;
type Vector3 = Bit.Inputs.Base.Vector3;
type TopoDSFacePointer = Bit.Inputs.OCCT.TopoDSFacePointer;
// Get access to OCCT face, point, and utility functions
const { face } = bitbybit.occt.shapes;
const { point } = bitbybit;
const { math, vector, json, lists } = bitbybit;
const { dimensions } = bitbybit.occt;
// Define the main function to create advanced hexagon face pattern
const start = async () => {
// Define grid parameters
const gridWidth = 16.5;
const gridHeight = 9;
const hexagonsInWidth = 29;
const hexagonsInHeight = 29;
const controlPointU = 0; // UV parameter for control point position
const controlPointV = 0.49; // UV parameter for control point position
// Create a reference rectangle face to define the control point
const rectangleOptions = new RectangleDto();
rectangleOptions.width = gridWidth;
rectangleOptions.length = gridHeight;
rectangleOptions.center = [0, 0, 0] as Point3;
rectangleOptions.direction = [0, 1, 0] as Vector3;
const rectangleFace = await face.createRectangleFace(rectangleOptions);
// Create control point on the rectangle face using UV parameters
const pointOnUVOptions = new DataOnUVDto<TopoDSFacePointer>();
pointOnUVOptions.shape = rectangleFace;
pointOnUVOptions.paramU = controlPointU;
pointOnUVOptions.paramV = controlPointV;
const controlPoint = await face.pointOnUV(pointOnUVOptions);
// Generate hexagon grid centers for distance calculation
const hexGridOptions = new HexGridScaledToFitDto();
hexGridOptions.width = gridWidth;
hexGridOptions.height = gridHeight;
hexGridOptions.nrHexagonsInWidth = hexagonsInWidth;
hexGridOptions.nrHexagonsInHeight = hexagonsInHeight;
hexGridOptions.flatTop = true;
hexGridOptions.extendTop = false;
hexGridOptions.extendBottom = false;
hexGridOptions.extendLeft = false;
hexGridOptions.extendRight = false;
hexGridOptions.centerGrid = true;
hexGridOptions.pointsOnGround = true;
const hexGrid = point.hexGridScaledToFit(hexGridOptions);
const hexCenters = hexGrid.centers;
// Calculate distances from control point to all hexagon centers
const distances = point.distancesToPoints({
startPoint: controlPoint,
endPoints: hexCenters
});
// Flatten the distance array and find min/max values
const minDistance = vector.min({ vector: distances });
const maxDistance = vector.max({ vector: distances });
// Remap distances to scale factors (0.211 to 0.9)
const remapOptions = new RemapNumberDto();
remapOptions.fromLow = minDistance;
remapOptions.fromHigh = maxDistance;
remapOptions.toLow = 0.211;
remapOptions.toHigh = 0.9;
const scalePattern = distances.map(x => {
remapOptions.number = x;
return math.remap(remapOptions);
})
// Create inclusion pattern for selective hexagon removal
const inclusionPattern = json.parse({ text: "[true, true, true, true, false]" });
// Create the hexagon faces with advanced patterns
const hexFaceOptions = new HexagonsInGridDto();
hexFaceOptions.width = gridWidth;
hexFaceOptions.height = gridHeight;
hexFaceOptions.nrHexagonsInWidth = hexagonsInWidth;
hexFaceOptions.nrHexagonsInHeight = hexagonsInHeight;
hexFaceOptions.flatTop = true;
hexFaceOptions.extendTop = false;
hexFaceOptions.extendBottom = false;
hexFaceOptions.extendLeft = false;
hexFaceOptions.extendRight = false;
hexFaceOptions.scalePatternWidth = scalePattern;
hexFaceOptions.scalePatternHeight = scalePattern;
hexFaceOptions.inclusionPattern = inclusionPattern;
const hexagonFaces = await face.hexagonsInGrid(hexFaceOptions);
// Create affector point visualization (control point elevated)
const affectorPoint = vector.add({
first: controlPoint,
second: [0, 3, 0] as Vector3
}) as Point3;
// Create pin with label to show the affector point
const pinOptions = new PinWithLabelDto();
pinOptions.startPoint = controlPoint;
pinOptions.endPoint = affectorPoint;
pinOptions.direction = [0, 0, 1] as Vector3;
pinOptions.offsetFromStart = 0.1;
pinOptions.label = "Affector";
pinOptions.labelOffset = 0.3;
pinOptions.labelSize = 0.1;
const pin = await dimensions.pinWithLabel(pinOptions);
// Draw the hexagon faces and affector pin
bitbybit.draw.drawAnyAsync({ entity: hexagonFaces });
bitbybit.draw.drawAnyAsync({ entity: pin });
// Optional: Draw the control point for reference
bitbybit.draw.drawAnyAsync({
entity: controlPoint,
});
}
// Execute the function
start();
How It Works
This example creates hexagonal faces that vary in size based on their distance from a control point, creating natural-looking patterns.
Step-by-Step Process
- Set up the grid parameters - Define width, height, and number of hexagons
- Create a control point - Use UV coordinates (0 to 1) to position it on the grid
- Calculate distances - Measure how far each hexagon center is from the control point
- Scale the hexagons - Closer hexagons become larger, distant ones become smaller
- Apply patterns - Optionally remove some hexagons to create openings
The Math Behind It
The key is remapping distances to scale values:
- Find the shortest and longest distances
- Convert these to scale factors between 0.211 and 0.9
- Apply these scales to make hexagons bigger or smaller
Why Use UV Coordinates?
UV coordinates (from 0 to 1) are better than exact positions because:
- U=0 means left edge, U=1 means right edge
- V=0 means bottom edge, V=1 means top edge
- Works the same regardless of grid size
- Easy to understand and adjust
Pattern Control
The inclusionPattern lets you remove hexagons in a repeating pattern:
[true, true, false]= show 2, skip 1, repeat[true, true, true, true, false]= show 4, skip 1, repeat
Real-World Uses
- Architecture: Building facades that respond to sunlight or wind
- Product Design: Grip patterns, ventilation holes, decorative surfaces
- Interior Design: Ceiling panels, wall textures, lighting patterns
The beauty of this approach is that simple distance calculations create complex, organic-looking patterns that feel natural rather than mechanical.