A java.awt.Paint implementation for triangular color interpolation (using barycentric coordinates). The svg file shows the result of the demo app (embedded image).

BarycentricGradientPaint.java

/* Copyright 2021 David Haegele - Source from JPlotter */

import java.awt.Color;
import java.awt.Paint;
import java.awt.PaintContext;
import java.awt.Rectangle;
import java.awt.RenderingHints;
import java.awt.Shape;
import java.awt.geom.AffineTransform;
import java.awt.geom.Point2D;
import java.awt.geom.Rectangle2D;
import java.awt.image.ColorModel;
import java.awt.image.DataBufferInt;
import java.awt.image.DirectColorModel;
import java.awt.image.Raster;
import java.awt.image.WritableRaster;
import java.lang.ref.WeakReference;

/**
 * The BarycentricGradientPaint class provides a way to fill a {@link Shape}
 * with a triangular color gradient. 
 * Colors are specified for the vertices of a triangle and interpolated within
 * the triangle according to barycentric coordinates.
 * Only areas of the filled shape that are intersecting with the triangle of
 * this paint are colored.
 * <p>
 * This paint supports the {@code ANTIALIASING} rendering hint 
 * ({@link RenderingHints}) using a 4x multisampling approach. 
 * When enabled, the edges of the triangle will appear anti-aliased.
 * It is recommended to disable AA when filling a triangle mesh (where triangles
 * are adjacent), since otherwise triangle edges become visible.
 * <p>
 * Note that it is not necessary to use a triangular {@link Shape} to render a 
 * triangle. Instead a rectangle can be used as well, since only the intersecting 
 * area will be filled.
 * 
 * @author hageldave
 */
public class BarycentricGradientPaint implements Paint {

	protected Point2D.Float p1;
	protected Point2D.Float p2;
	protected Point2D.Float p3;
	protected Color color1;
	protected Color color2;
	protected Color color3;


	/**
	 * Creates a new {@link BarycentricGradientPaint} object with
	 * specified triangle vertices and vertex colors.
	 * 
	 * @param p1 vertex of triangle
	 * @param p2 vertex of triangle
	 * @param p3 vertex of triangle
	 * @param color1 color of vertex
	 * @param color2 color of vertex
	 * @param color3 color of vertex
	 */
	public BarycentricGradientPaint(Point2D p1, Point2D p2, Point2D p3, Color color1, Color color2, Color color3) {
		this.p1 = new Point2D.Float((float)p1.getX(), (float)p1.getY());
		this.p2 = new Point2D.Float((float)p2.getX(), (float)p2.getY());
		this.p3 = new Point2D.Float((float)p3.getX(), (float)p3.getY());
		this.color1 = color1;
		this.color2 = color2;
		this.color3 = color3;
	}

	/**
	 * Creates a new {@link BarycentricGradientPaint} object with
	 * specified triangle vertices and vertex colors.
	 * 
	 * @param x x-coordinates for the triangle vertices
	 * @param y y-coordinates for the triangle vertices
	 * @param color1 color of vertex
	 * @param color2 color of vertex
	 * @param color3 color of vertex
	 */
	public BarycentricGradientPaint(float[] x, float[] y, Color color1, Color color2, Color color3) {
		this(x[0],y[0],x[1],y[1],x[2],y[2], color1,color2,color3);
	}

	/**
	 * Creates a new {@link BarycentricGradientPaint} object with
	 * specified triangle vertices and vertex colors.
	 * 
	 * @param x1 x-coord of triangle vertex
	 * @param y1 y-coord of triangle vertex
	 * @param x2 x-coord of triangle vertex
	 * @param y2 y-coord of triangle vertex
	 * @param x3 x-coord of triangle vertex
	 * @param y3 y-coord of triangle vertex
	 * @param color1 color of vertex
	 * @param color2 color of vertex
	 * @param color3 color of vertex
	 */
	public BarycentricGradientPaint(double x1, double y1, double x2, double y2, double x3, double y3, Color color1, Color color2, Color color3) {
		this((float)x1,(float)y1,(float)x2,(float)y2,(float)x3,(float)y3, color1,color2,color3);
	}

	/**
	 * Creates a new {@link BarycentricGradientPaint} object with
	 * specified triangle vertices and vertex colors.
	 * 
	 * @param x1 x-coord of triangle vertex
	 * @param y1 y-coord of triangle vertex
	 * @param x2 x-coord of triangle vertex
	 * @param y2 y-coord of triangle vertex
	 * @param x3 x-coord of triangle vertex
	 * @param y3 y-coord of triangle vertex
	 * @param color1 color of vertex
	 * @param color2 color of vertex
	 * @param color3 color of vertex
	 */
	public BarycentricGradientPaint(float x1, float y1, float x2, float y2, float x3, float y3, Color color1, Color color2, Color color3) {
		this.p1 = new Point2D.Float(x1, y1);
		this.p2 = new Point2D.Float(x2, y2);
		this.p3 = new Point2D.Float(x3, y3);
		this.color1 = color1;
		this.color2 = color2;
		this.color3 = color3;
	}



	@Override
	public int getTransparency() {
		int a1 = color1.getAlpha();
		int a2 = color2.getAlpha();
		int a3 = color3.getAlpha();
		return (((a1 & a2 & a3) == 0xff) ? OPAQUE : TRANSLUCENT);
	}


	@Override
	public PaintContext createContext(ColorModel cm, Rectangle deviceBounds, Rectangle2D userBounds,
			AffineTransform xform, RenderingHints hints) {
		return new BarycentricGradientPaintContext(
				p1,p2,p3, 
				color1,color2,color3, 
				xform, 
				hints.get(RenderingHints.KEY_ANTIALIASING) == RenderingHints.VALUE_ANTIALIAS_ON
		);
	}

	/**
	 * This class is implements the {@link PaintContext} for 
	 * {@link BarycentricGradientPaint}.
	 * <p>
	 * The context operates solely in ARGB color space (blue on least 
	 * significant bits) with an integer packing {@link DirectColorModel}.
	 * <p>
	 * A cache for raster memory is implemented to avoid costly memory 
	 * allocations.
	 * 
	 * @author hageldave
	 */
	public static class BarycentricGradientPaintContext implements PaintContext {
		protected static final float[] MSAA_SAMPLES;

		static {
			MSAA_SAMPLES = new float[8];
			AffineTransform xform = new AffineTransform();
			xform.translate(.5, .5);
			xform.rotate(Math.PI*0.5*0.2);
			xform.scale(.5, .5);
			xform.translate(-.5, -.5);
			xform.transform(new float[] {0,0, 1,0, 0,1, 1,1}, 0, MSAA_SAMPLES, 0, 4);
		}

		protected final float x1,x2,x3,y1,y2,y3;
		protected final float x23,x13,y23,y13; //,x12,y12;
		protected final float denom;

		protected final int c1,c2,c3;
		protected final DirectColorModel cm = new DirectColorModel(32,
				0x00ff0000,       // Red
				0x0000ff00,       // Green
				0x000000ff,       // Blue
				0xff000000        // Alpha
				);
		protected final boolean antialiasing;
		protected WritableRaster saved;
		protected WeakReference<int[]> cache;

		public BarycentricGradientPaintContext(
				Point2D.Float p1, Point2D.Float p2, Point2D.Float p3,
				Color color1, Color color2, Color color3,
				AffineTransform xform, boolean antialiasing) 
		{
			c1 = color1.getRGB();
			c2 = color2.getRGB();
			c3 = color3.getRGB();

			p1 = (Point2D.Float) xform.transform(p1, new Point2D.Float());
			p2 = (Point2D.Float) xform.transform(p2, new Point2D.Float());
			p3 = (Point2D.Float) xform.transform(p3, new Point2D.Float());
			// constants for barycentric coords
			x1=p1.x; x2=p2.x; x3=p3.x; y1=p1.y; y2=p2.y; y3=p3.y;
			x23=x2-x3; x13=x1-x3; y23=y2-y3; y13=y1-y3; // x12=x1-x2; y12=y1-y2;
			denom=1f/((y23*x13)-(x23*y13));
			
			this.antialiasing = antialiasing;
		}


		@Override
		public void dispose() {
			if(saved != null)
				cacheRaster(saved);
			saved = null;
		}

		@Override
		public ColorModel getColorModel() {
			return cm;
		}

		@Override
		public Raster getRaster(int xA, int yA, int w, int h) {
			WritableRaster rast = saved;
			if (rast == null) {
				rast = getCachedOrCreateRaster(w, h);
				saved = rast;
			} else if(rast.getWidth() != w || rast.getHeight() != h) {
				int[] data = dataFromRaster(rast);
				if(data.length < w*h) {
					data = new int[w*h];
				}
				rast = createRaster(w, h, data);
				saved = rast;
			}

			// fill data array with interpolated colors (barycentric coords)
			int[] data = dataFromRaster(rast);
			if(antialiasing)
				fillRasterMSAA(xA, yA, w, h, data);
			else
				fillRaster(xA, yA, w, h, data);


			return rast;
		}

		protected void fillRaster(int xA, int yA, int w, int h, int[] data) {
			for(int i=0; i<h; i++) {
				float y = yA+i+.5f;
				float ypart11 = -x23*(y-y3);
				float ypart21 =  x13*(y-y3);
		
				for(int j=0; j<w; j++) {
					float x = xA+j+.5f;
					// calculate barycentric coordinates for (x,y)
					float l1 = ( y23*(x-x3)+ypart11)*denom;
					float l2 = (-y13*(x-x3)+ypart21)*denom;
					float l3 = 1f-l1-l2;
		
					// determine color
					int mix1;
					if(l1<0||l2<0||l3<0) mix1 = 0;
					else mix1 = mixColor3(c1, c2, c3, l1, l2, l3);
					data[i*w+j] = mix1;
				}
			}
		}


		protected void fillRasterMSAA(int xA, int yA, int w, int h, int[] data) {
			for(int i=0; i<h; i++) {
				float y = yA+i+MSAA_SAMPLES[1];
				float ypart11 = -x23*(y-y3);
				float ypart21 =  x13*(y-y3);
				y = yA+i+MSAA_SAMPLES[3];
				float ypart12 = -x23*(y-y3);
				float ypart22 =  x13*(y-y3);
				y = yA+i+MSAA_SAMPLES[5];
				float ypart13 = -x23*(y-y3);
				float ypart23 =  x13*(y-y3);
				y = yA+i+MSAA_SAMPLES[7];
				float ypart14 = -x23*(y-y3);
				float ypart24 =  x13*(y-y3);

				for(int j=0; j<w; j++) {
					float x = xA+j+MSAA_SAMPLES[0];
					float xpart11 =  y23*(x-x3);
					float xpart21 = -y13*(x-x3);
					x = xA+j+MSAA_SAMPLES[2];
					float xpart12 =  y23*(x-x3);
					float xpart22 = -y13*(x-x3);
					x = xA+j+MSAA_SAMPLES[4];
					float xpart13 =  y23*(x-x3);
					float xpart23 = -y13*(x-x3);
					x = xA+j+MSAA_SAMPLES[6];
					float xpart14 =  y23*(x-x3);
					float xpart24 = -y13*(x-x3);

					// calculate barycentric coordinates for the 4 sub pixel samples
					float l11 = (xpart11+ypart11)*denom;
					float l21 = (xpart21+ypart21)*denom;
					float l31 = 1f-l11-l21;

					float l12 = (xpart12+ypart12)*denom;
					float l22 = (xpart22+ypart22)*denom;
					float l32 = 1f-l12-l22;

					float l13 = (xpart13+ypart13)*denom;
					float l23 = (xpart23+ypart23)*denom;
					float l33 = 1f-l13-l23;

					float l14 = (xpart14+ypart14)*denom;
					float l24 = (xpart24+ypart24)*denom;
					float l34 = 1f-l14-l24;

					// determine sample colors and weights (out of triangle samples have 0 weight)
					int mix1,mix2,mix3,mix4;
					float w1,w2,w3,w4;

					if(l11<0||l21<0||l31<0) { mix1 = 0; w1=0f; }
					else { mix1 = mixColor3(c1, c2, c3, l11, l21, l31); w1=1f; }

					if(l12<0||l22<0||l32<0) { mix2 = 0; w2=0f; }
					else { mix2 = mixColor3(c1, c2, c3, l12, l22, l32); w2=1f; }

					if(l13<0||l23<0||l33<0) {mix3 = 0; w3=0f; }
					else { mix3 = mixColor3(c1, c2, c3, l13, l23, l33); w3=1f; }

					if(l14<0||l24<0||l34<0) { mix4 = 0; w4=0f; }
					else { mix4 = mixColor3(c1, c2, c3, l14, l24, l34); w4=1f; }

					int color = mixColor4(mix1, mix2, mix3, mix4, w1,w2,w3,w4);
					data[i*w+j] = scaleColorAlpha(color,(w1+w2+w3+w4)*.25f);
				}
			}
		}

		protected WritableRaster getCachedOrCreateRaster(int w, int h) {
			if(cache != null) {
				int[] data = cache.get();
				if (data != null && data.length >= w*h)
				{
					cache = null;
					return createRaster(w, h, data);
				}
			}
			return createRaster(w, h, new int[w*h]);
		}

		protected void cacheRaster(WritableRaster ras) {
			int[] toCache = dataFromRaster(ras);
			if (cache != null) {
				int[] data = cache.get();
				if (data != null) {
					if (toCache.length < data.length) {
						return;
					}
				}
			}
			cache = new WeakReference<>(toCache);
		}

		protected WritableRaster createRaster(int w, int h, int[] data) {
			DataBufferInt buffer = new DataBufferInt(data, w*h);
			WritableRaster raster = Raster.createPackedRaster(buffer, w, h, w, cm.getMasks(), null);
			return raster;
		}

		private static int[] dataFromRaster(WritableRaster wr) {
			return ((DataBufferInt)wr.getDataBuffer()).getData();
		}
		
		private static int mixColor3(int c1, int c2, int c3, float m1, float m2, float m3) {
			float normalize = 1f/(m1+m2+m3);
			float a = (a(c1)*m1 + a(c2)*m2 + a(c3)*m3)*normalize;
			float r = (r(c1)*m1 + r(c2)*m2 + r(c3)*m3)*normalize;
			float g = (g(c1)*m1 + g(c2)*m2 + g(c3)*m3)*normalize;
			float b = (b(c1)*m1 + b(c2)*m2 + b(c3)*m3)*normalize;
			return argb((int)a, (int)r, (int)g, (int)b);
		}
		
		private static int mixColor4(int c1, int c2, int c3, int c4, float m1, float m2, float m3, float m4) {
			float normalize = 1f/(m1+m2+m3+m4);
			float a = (a(c1)*m1 + a(c2)*m2 + a(c3)*m3 + a(c4)*m4)*normalize;
			float r = (r(c1)*m1 + r(c2)*m2 + r(c3)*m3 + r(c4)*m4)*normalize;
			float g = (g(c1)*m1 + g(c2)*m2 + g(c3)*m3 + g(c4)*m4)*normalize;
			float b = (b(c1)*m1 + b(c2)*m2 + b(c3)*m3 + b(c4)*m4)*normalize;
			return argb((int)a, (int)r, (int)g, (int)b);
		}
		
		private static int a(int argb) {
			return (argb >> 24) & 0xff;
		}
		
		private static int r(int argb) {
			return (argb >> 16) & 0xff;
		}
		
		private static int g(int argb) {
			return (argb >> 8) & 0xff;
		}
		
		private static int b(int argb) {
			return (argb) & 0xff;
		}
		
		private static int argb(final int a, final int r, final int g, final int b){
			return (a<<24)|(r<<16)|(g<<8)|b;
		}
		
		private static int scaleColorAlpha(int color, float m) {
			float normalize = 1f/255f;
			float af = a(color)*normalize*m;
			int a = (((int)(af*255f)) & 0xff) << 24;
			return (color&0x00ffffff)|a;
		}

	}


}

DemoResult.svg

TriangularColorInterpolationDemo.java

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;

import javax.swing.JComponent;
import javax.swing.JFrame;
import javax.swing.SwingUtilities;

public class TriangularColorInterpolationDemo {

	public static void main(String[] args) {
		JComponent triangleDisplay = new JComponent() {
			private static final long serialVersionUID = 1L;

			@Override
			public void paint(Graphics g) {
				super.paint(g);
				Graphics2D g2d = (Graphics2D)g;
				
				g2d.setPaint(new BarycentricGradientPaint(20, 100, 100, 120, 60, 20, Color.red, Color.green, Color.blue));
				g2d.fillRect(20, 20, 100, 100);
				
				g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
				g2d.setPaint(new BarycentricGradientPaint(100, 20, 170, 70, 70, 120, Color.yellow, Color.cyan, new Color(0x44ff00ff, true)));
				g2d.fillRect(70, 20, 100, 100);
			}
		};
		triangleDisplay.setPreferredSize(new Dimension(180, 150));
		
		JFrame frame = new JFrame();
		frame.getContentPane().add(triangleDisplay);
		frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
		SwingUtilities.invokeLater(()->{
			frame.pack();
			frame.setVisible(true);
		});
	}
	
}