摘要：Non-linear curve: Achieves more complex adjustments through power functions, logarithmic functions, etc. (such as gamma correction
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思维导图
Mind mapping
剪辑曲线原理
Principles of Editing Curves
一、数学模型与映射关系
I. Mathematical Model and Mapping Relationship
1. 输入与输出映射
1.Input and Output Mapping
曲线通过横轴（输入值）和纵轴（输出值）的映射关系，将原始像素值重新计算为目标值。例如：
The curve uses the mapping relationship between the horizontal axis (input values) and the vertical axis (output values) to recalculate the original pixel values into target values. For example:
线性曲线：简单调整整体亮度（如提亮或压暗）。
Linear curve: Simply adjusts the overall brightness (such as brightening or darkening).
非线性曲线：通过幂函数、对数函数等实现更复杂的调整（如伽马校正）。
Non-linear curve: Achieves more complex adjustments through power functions, logarithmic functions, etc. (such as gamma correction).
2. 直方图与色阶
2.Histogram and Tonal Levels
曲线基于直方图原理，将图像分为暗部（0-63）、中间调（64-191）、亮部（192-255）三部分。调整曲线时，可针对性地改变特定区域的像素分布。
The curve is based on the histogram principle, dividing the image into three parts: shadows (0-63), midtones (64-191), and highlights (192-255). When adjusting the curve, you can selectively change the pixel distribution in specific areas.
二、控制点与插值算法
II. Control Points and Interpolation Algorithms
1. 控制点定义曲线形状
1.Control Points Define Curve Shape
用户通过添加、移动控制点（锚点）定义曲线形态。例如：
Users define the shape of the curve by adding and moving control points (anchors). For example:
S形曲线：左侧下拉（暗部压暗）、右侧上扬（亮部提亮），增强对比度。
S-shaped curve: Pull down on the left side (darken shadows) and lift up on the right side (brighten highlights) to enhance Contrast.
胶片曲线：两端轻微调整（暗部不压死、亮部不过曝），模拟胶片柔和质感。
Film curve: Slightly adjust both ends (avoid crushing shadows and blowing out highlights) to simulate the soft texture of film.
2. 插值算法实现平滑过渡
2.Interpolation Algorithms Achieve Smooth Transitions
控制点间通过插值算法（如线性插值、样条插值）生成平滑曲线，确保调整效果自然。样条插值尤其适用于复杂动画或视频变速中的细腻过渡。
Interpolation algorithms (such as linear interpolation and spline interpolation) are used between control points to generate smooth curves, ensuring a natural adjustment effect. Spline interpolation is especially suitable for delicate transitions in complex Animations or video speed adjustments.
三、颜色通道与分层调整
III. Color Channels and Layered Adjustments
1. 独立通道控制
1.Independent Channel Control
曲线可分别作用于RGB（红、绿、蓝）或HSV通道，实现精准色彩校正：
The curve can act on RGB (red, green, blue) or HSV channels separately to achieve precise color correction:
单色调整：如提亮红色通道增强画面暖调。
Single-color adjustment: For example, brightening the red channel to enhance the warm tone of the image.
互补色平衡 ：通过降低绿色通道减少洋红偏色（绿色与洋红互为补色）。
Complementary color balance: Reduce the green channel to decrease magenta color cast (green and magenta are complementary colors).
2. 综合通道应用
2.Combined Channel Application
多通道组合可创造丰富效果，例如：
Combining multiple channels can create rich effects, such as:
冷色调：降低红色通道高光，提升蓝色通道暗部。
Cool tone: Lower the red channel highlights and boost the blue channel shadows.
复古风格：压低蓝色通道整体值，增加黄色（蓝色补色）。
Retro style: Lower the overall value of the blue channel and increase yellow (the complementary color of blue).
四、实际应用场景
IV. Practical Application Scenarios
1. 基础调色
1.Basic Color Adjustment
亮度调整：通过整体曲线上下移动控制明暗。
Brightness adjustment: Control brightness by moving the entire curve up or down.
对比度优化：S形曲线强化明暗对比。
Contrast optimization: Enhance the contrast between light and dark with an S-shaped curve.
2. 色彩校正
2.Color Correction
修正偏色（如增加绿色通道校正洋红偏色）。
Color correction: Correct color casts (such as increasing the green channel to correct magenta color casts).
风格化调色（如“赛博朋克”风格通过高饱和红绿通道叠加）。
Stylized coloring: For example, the "cyberpunk" style through high-saturation red and green channel overlays.
3. 动态效果
3.Dynamic Effects
曲线变速：在视频剪辑中通过时间轴曲线实现慢动作、快切或渐变速度。
Curve-based speed adjustment： Achieve slow motion, fast cuts, or gradual speed changes in video editing through timeline curves.
动画过渡：在Unity等软件中控制角色运动的缓入/缓出效果。
Animation transition: Control the ease-in and ease-out effects of character movements in software like Unity.
五、工具差异与技巧
V. Tool Differences and Techniques
不同软件（如剪映、PS、达芬奇）的曲线工具略有差异，但核心逻辑一致：
Curve tools in different software (such as CapCut, Photoshop, and DaVinci Resolve) vary slightly, but the core logic is the same:
剪映：提供亮度、RGB通道独立调节，支持通过“小手”工具直接点击画面局部调整。
CapCut: Offers independent brightness and RGB channel adjustments, and supports direct local adjustments in the image through the "hand" tool.
PS：支持16个锚点，可精细控制曲线形状，适合静态图像的专业修图。
Photoshop: Supports 16 anchors for precise curve shape control, suitable for professional static image editing.
达芬奇：结合色轮与曲线，适合复杂视频调色。
DaVinci Resolve: Combines color wheels and curves, suitable for complex video color grading.
总结：剪辑曲线通过数学映射、控制点编辑和通道分离，赋予创作者对媒体属性的极致控制权。掌握其原理后，可灵活应用于调色、动画、变速等场景，显著提升作品的表现力。
Summary: Editing curves, through mathematical mapping, control point editing, and channel separation, give creators ultimate control over media properties. Once you master the principles, you can flexibly apply them to color grading, animation, speed adjustment, and other scenarios, significantly enhancing the expressiveness of your work.
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