在基于瓷砖的游戏中围绕玩家照明

Question

我正在使用 Java 开发一个基于瓷砖的挖掘游戏，我想在玩家周围使用渐变照明，想想 Terraria。我目前只是将图像与一个矩形重叠，其中该矩形上的 alpha 是我希望拥有的亮度（0.01 = 黑色，1 = 明亮），这可以正常工作。这不是我如何设置我需要帮助的照明，而是如何编写一个紧凑而有效的算法，让我的数字越大，方块离玩家越近，数字越小，方块离玩家越远.该数字应在 (1 - 0.01) 范围内。每次玩家移动时，我都会调用以下方法：

public void calculateBlockBrightness(int playerInRow, int playerInCol) {

    int affectedBlocks = 5;
    float brightness;

    // Loops through all blocks within (affectedBlocks) blocks of the player
    for (int row = playerInRow - affectedBlocks; row <= playerInRow + affectedBlocks; row++) {
        for (int col = playerInCol - affectedBlocks; col <= playerInCol + affectedBlocks; col++) {

            // Not all blocks should be affected by this method
            if (blockNotRelevantForBrightness(row, col))
                continue;

            // If the block is within (affectedBlocks - 1) blocks of the player
            if (row >= playerInRow - (affectedBlocks - 1) && row <= playerInRow + (affectedBlocks - 1)
                    && col >= playerInCol - (affectedBlocks - 1) && col <= playerInCol + (affectedBlocks - 1)) {

                /*
                 * Algorithm
                 */

                blocks[row][col].setBrightnessPercentage(brightness);

            // Reset the "outer layer" blocks to default brightness.
            } else {
                blocks[row][col].setBrightnessPercentage(blocks[row][col].getBrightnessDefault());

            }
        }
    }
}

Answer 1

在这种情况下，分两步计算所需值通常是有益的：

1. 计算 [0...1] 范围内的插值
2. 根据插值在最小值和最大值之间进行插值

这里的插值是一个“相对”的距离，用于在最小和最大亮度之间进行插值。

两个图块之间的距离可以计算为

sqrt(rowDifference² + columnDifference²)

（顺便说一句，这可以方便地使用Math#hypot 计算）。

受影响的图块与玩家图块在水平和垂直方向上的最大距离为(affectedBlocks - 1)。对于一对瓦片，即瓦片(row, col) 和(playerInRow, playerInCol)，现在可以计算这些瓦片之间的距离，然后将其除以最大距离，以获得作为[0,1] 中的值的相对距离。该值可用于计算适当的亮度。

private float computeBrightness(
    int row, int col, int playerRow, int playerCol, int affectedBlocks)
{
    // Compute the distance of the tile (row, col) to the player tile
    double distance = Math.hypot(row - playerRow, col - playerCol);

    // Compute the maximum possible distance of a tile
    double maxDistance = Math.hypot(affectedBlocks - 1, affectedBlocks -1);

    // Compute the relative distance, as a value in [0,1]
    double relative = distance / maxDistance;

    // Compute the brightness for the relative distance
    double minBrightness = 0.01;
    double maxBrightness = 1.0;
    double brightness = 
        maxBrightness - relative * (maxBrightness - minBrightness);

    System.out.println(
        "For " + row + " " + col + " brightness is " + brightness);

    return (float)brightness;
}

---

附注：假设affectedBlocks 是常数，最大距离也是常数，并且可以存储为常数值字段，例如

private static final int AFFECTED_BLOCKS = 5;
private static final double MAX_DISTANCE = 
    Math.hypot(AFFECTED_BLOCKS - 1, AFFECTED_BLOCKS - 1);