org.joml.Interpolationf Maven / Gradle / Ivy
/*
* The MIT License
*
* Copyright (c) 2015-2019 Kai Burjack
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* THE SOFTWARE.
*/
package org.joml;
/**
* Contains various interpolation functions.
*
* @author Kai Burjack
*/
public class Interpolationf {
/**
* Bilinearly interpolate the single scalar value f over the given triangle.
*
* Reference: https://en.wikipedia.org/
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param f0
* the value of f at the first vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param f1
* the value of f at the second vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param f2
* the value of f at the third vertex
* @param x
* the x coordinate of the point to interpolate f at
* @param y
* the y coordinate of the point to interpolate f at
* @return the interpolated value of f
*/
public static float interpolateTriangle(
float v0X, float v0Y, float f0,
float v1X, float v1Y, float f1,
float v2X, float v2Y, float f2,
float x, float y) {
float v12Y = v1Y - v2Y;
float v21X = v2X - v1X;
float v02X = v0X - v2X;
float yv2Y = y - v2Y;
float xv2X = x - v2X;
float v02Y = v0Y - v2Y;
float invDen = 1.0f / (v12Y * v02X + v21X * v02Y);
float l1 = (v12Y * xv2X + v21X * yv2Y) * invDen;
float l2 = (v02X * yv2Y - v02Y * xv2X) * invDen;
return l1 * f0 + l2 * f1 + (1.0f - l1 - l2) * f2;
}
/**
* Bilinearly interpolate the two-dimensional vector f over the given triangle and store the result in dest.
*
* Reference: https://en.wikipedia.org/
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param f0X
* the x component of the value of f at the first vertex
* @param f0Y
* the y component of the value of f at the first vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param f1X
* the x component of the value of f at the second vertex
* @param f1Y
* the y component of the value of f at the second vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param f2X
* the x component of the value of f at the third vertex
* @param f2Y
* the y component of the value of f at the third vertex
* @param x
* the x coordinate of the point to interpolate f at
* @param y
* the y coordinate of the point to interpolate f at
* @param dest
* will hold the interpolation result
* @return dest
*/
public static Vector2f interpolateTriangle(
float v0X, float v0Y, float f0X, float f0Y,
float v1X, float v1Y, float f1X, float f1Y,
float v2X, float v2Y, float f2X, float f2Y,
float x, float y, Vector2f dest) {
float v12Y = v1Y - v2Y;
float v21X = v2X - v1X;
float v02X = v0X - v2X;
float yv2Y = y - v2Y;
float xv2X = x - v2X;
float v02Y = v0Y - v2Y;
float invDen = 1.0f / (v12Y * v02X + v21X * v02Y);
float l1 = (v12Y * xv2X + v21X * yv2Y) * invDen;
float l2 = (v02X * yv2Y - v02Y * xv2X) * invDen;
float l3 = 1.0f - l1 - l2;
dest.x = l1 * f0X + l2 * f1X + l3 * f2X;
dest.y = l1 * f0Y + l2 * f1Y + l3 * f2Y;
return dest;
}
/**
* Compute the first-order derivative of a linear two-dimensional function f with respect to X
* and store the result in dest.
*
* This method computes the constant rate of change for f given the three values of f
* at the specified three inputs (v0X, v0Y), (v1X, v1Y) and (v2X, v2Y).
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param f0X
* the x component of the value of f at the first vertex
* @param f0Y
* the y component of the value of f at the first vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param f1X
* the x component of the value of f at the second vertex
* @param f1Y
* the y component of the value of f at the second vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param f2X
* the x component of the value of f at the third vertex
* @param f2Y
* the y component of the value of f at the third vertex
* @param dest
* will hold the result
* @return dest
*/
public static Vector2f dFdxLinear(
float v0X, float v0Y, float f0X, float f0Y,
float v1X, float v1Y, float f1X, float f1Y,
float v2X, float v2Y, float f2X, float f2Y, Vector2f dest) {
float v12Y = v1Y - v2Y;
float v02Y = v0Y - v2Y;
float den = v12Y * (v0X - v2X) + (v2X - v1X) * v02Y;
float l3_1 = den - v12Y + v02Y;
float invDen = 1.0f / den;
dest.x = invDen * (v12Y * f0X - v02Y * f1X + l3_1 * f2X) - f2X;
dest.y = invDen * (v12Y * f0Y - v02Y * f1Y + l3_1 * f2Y) - f2Y;
return dest;
}
/**
* Compute the first-order derivative of a linear two-dimensional function f with respect to Y
* and store the result in dest.
*
* This method computes the constant rate of change for f given the three values of f
* at the specified three inputs (v0X, v0Y), (v1X, v1Y) and (v2X, v2Y).
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param f0X
* the x component of the value of f at the first vertex
* @param f0Y
* the y component of the value of f at the first vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param f1X
* the x component of the value of f at the second vertex
* @param f1Y
* the y component of the value of f at the second vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param f2X
* the x component of the value of f at the third vertex
* @param f2Y
* the y component of the value of f at the third vertex
* @param dest
* will hold the result
* @return dest
*/
public static Vector2f dFdyLinear(
float v0X, float v0Y, float f0X, float f0Y,
float v1X, float v1Y, float f1X, float f1Y,
float v2X, float v2Y, float f2X, float f2Y,
Vector2f dest) {
float v21X = v2X - v1X;
float v02X = v0X - v2X;
float den = (v1Y - v2Y) * v02X + v21X * (v0Y - v2Y);
float l3_1 = den - v21X - v02X;
float invDen = 1.0f / den;
dest.x = invDen * (v21X * f0X + v02X * f1X + l3_1 * f2X) - f2X;
dest.y = invDen * (v21X * f0Y + v02X * f1Y + l3_1 * f2Y) - f2Y;
return dest;
}
/**
* Bilinearly interpolate the three-dimensional vector f over the given triangle and store the result in dest.
*
* Reference: https://en.wikipedia.org/
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param f0X
* the x component of the value of f at the first vertex
* @param f0Y
* the y component of the value of f at the first vertex
* @param f0Z
* the z component of the value of f at the first vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param f1X
* the x component of the value of f at the second vertex
* @param f1Y
* the y component of the value of f at the second vertex
* @param f1Z
* the z component of the value of f at the second vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param f2X
* the x component of the value of f at the third vertex
* @param f2Y
* the y component of the value of f at the third vertex
* @param f2Z
* the z component of the value of f at the third vertex
* @param x
* the x coordinate of the point to interpolate f at
* @param y
* the y coordinate of the point to interpolate f at
* @param dest
* will hold the interpolation result
* @return dest
*/
public static Vector3f interpolateTriangle(
float v0X, float v0Y, float f0X, float f0Y, float f0Z,
float v1X, float v1Y, float f1X, float f1Y, float f1Z,
float v2X, float v2Y, float f2X, float f2Y, float f2Z,
float x, float y, Vector3f dest) {
// compute interpolation factors
Vector3f t = dest;
interpolationFactorsTriangle(v0X, v0Y, v1X, v1Y, v2X, v2Y, x, y, t);
// interpolate using these factors
return dest.set(t.x * f0X + t.y * f1X + t.z * f2X,
t.x * f0Y + t.y * f1Y + t.z * f2Y,
t.x * f0Z + t.y * f1Z + t.z * f2Z);
}
/**
* Compute the interpolation factors (t0, t1, t2) in order to interpolate an arbitrary value over a given
* triangle at the given point (x, y).
*
* This method takes in the 2D vertex positions of the three vertices of a triangle and stores in dest the
* factors (t0, t1, t2) in the equation v' = v0 * t0 + v1 * t1 + v2 * t2 where (v0, v1, v2) are
* arbitrary (scalar or vector) values associated with the respective vertices of the triangle. The computed value v'
* is the interpolated value at the given position (x, y).
*
* @param v0X
* the x coordinate of the first triangle vertex
* @param v0Y
* the y coordinate of the first triangle vertex
* @param v1X
* the x coordinate of the second triangle vertex
* @param v1Y
* the y coordinate of the second triangle vertex
* @param v2X
* the x coordinate of the third triangle vertex
* @param v2Y
* the y coordinate of the third triangle vertex
* @param x
* the x coordinate of the point to interpolate at
* @param y
* the y coordinate of the point to interpolate at
* @param dest
* will hold the interpolation factors (t0, t1, t2)
* @return dest
*/
public static Vector3f interpolationFactorsTriangle(
float v0X, float v0Y, float v1X, float v1Y, float v2X, float v2Y,
float x, float y, Vector3f dest) {
float v12Y = v1Y - v2Y;
float v21X = v2X - v1X;
float v02X = v0X - v2X;
float yv2Y = y - v2Y;
float xv2X = x - v2X;
float v02Y = v0Y - v2Y;
float invDen = 1.0f / (v12Y * v02X + v21X * v02Y);
dest.x = (v12Y * xv2X + v21X * yv2Y) * invDen;
dest.y = (v02X * yv2Y - v02Y * xv2X) * invDen;
dest.z = 1.0f - dest.x - dest.y;
return dest;
}
}