📚 Year 9 Edexcel Art: Formula and Theorem Quick Reference Handbook | 九年级 Edexcel 艺术：公式定理速查手册
Art is often seen as a subject of pure creativity, yet it is built upon a solid foundation of visual 'formulas' and principles. From the mathematical ratios of composition to the systematic rules of colour mixing and perspective, understanding these core theorems gives every young artist a powerful toolkit. This quick reference handbook compiles the essential formulas, rules, and ratios you need for the Year 9 Edexcel Art course, presented in a clear bilingual format for easy revision.
艺术常被视为纯粹创意的学科，但它其实建立在一系列视觉“公式”与原理的坚实基础之上。从构图中的数学比例，到色彩混合与透视的系统规则，掌握这些核心定理能让每位年轻艺术学子获得强大的创作工具。本速查手册汇编了九年级 Edexcel 艺术课程所需的关键公式、法则与比例，以清晰的双语形式呈现，方便复习与查阅。
1. The Colour Wheel & Primary Colours | 色轮与三原色
The colour wheel is a circular diagram that organises hues by their chromatic relationship. The three primary colours in traditional art are red, yellow, and blue. They cannot be created by mixing any other colours and form the starting point for all colour theory.
色轮是一种圆形图示，根据色相之间的色彩关系进行排列。传统艺术中的三原色是红、黄、蓝。它们无法通过混合其他任何颜色得到，是所有色彩理论的起点。
he simple formulas are: Red + Yellow = Orange; Yellow + Blue = Green; Blue + Red = Violet.
间色是通过等比例混合两种原色得到的。简单的公式为：红 + 黄 = 橙；黄 + 蓝 = 绿；蓝 + 红 = 紫。
Tertiary colours result from mixing a primary with an adjacent secondary, giving six more hues such as red-orange and blue-green.
复色由一种原色和其相邻的间色混合而成，共产生六种色相，例如红橙、蓝绿等。
2. Colour Schemes (Harmonies) | 色彩调和公式
A colour scheme is a planned combination of colours that creates a specific visual effect. The following 'formulas' are the most reliable harmonies used in art and design.
色彩调和方案是一种有计划的色彩组合，能创造特定的视觉效果。以下“公式”是艺术与设计中最可靠的配色法则。
- Complementary: Two colours directly opposite on the colour wheel. Examples: Red + Green, Blue + Orange, Yellow + Purple. This scheme creates maximum contrast and vibrancy.
- 互补色: 色轮上直接相对的两种颜色。例如：红 + 绿，蓝 + 橙，黄 + 紫。该方案产生最大的对比与活力。
- Analogous: Three to five colours that sit side by side on the wheel, such as Yellow, Yellow-Green, Green. This formula yields a calm and unified feel.
- 类似色: 色轮上相邻的三至五种颜色，例如黄、黄绿、绿。该公式产生宁静而统一的感受。
- Triadic: Three colours evenly spaced around the wheel, such as Red, Yellow, Blue. The result is bold and balanced.
- 三角色: 在色轮上均匀分布的三种颜色，例如红、黄、蓝。效果鲜明而平衡。
- Split-Complementary: One base colour plus the two colours adjacent to its complement. For instance, Blue with Yellow-Orange and Red-Orange. A softer contrast than direct complements.
- 分裂互补色: 一种基础色加上其互补色两边的两个颜色。例如，蓝搭配黄橙与红橙。对比比直接互补色更柔和。
3. Subtractive Colour Mixing Formula | 减色混合公式
When working with paints, inks, or pencils, you are using subtractive mixing. Light is absorbed (subtracted) by the pigments, and the reflected light determines the colour we see. The basic formulas for mixing secondary colours from primaries are central to every artist's palette.
在使用颜料、墨水或铅笔时，你所进行的是减色混合。光线被颜料吸收（减去），反射出的光决定了我们看到的颜色。由原色混合得到间色的基本公式是每位艺术家调色盘的核心。
Red + Yellow = Orange
红 + 黄 = 橙
Yellow + Blue = Green
黄 + 蓝 = 绿
Blue + Red = Violet
蓝 + 红 = 紫
To darken a colour, add a small amount of its complement, which acts as a natural 'blackening' formula. Adding white produces a tint; adding black produces a shade; adding grey produces a tone.
要加深一种颜色，可加入少量它的互补色，这相当于一种天然的“变暗”公式。加入白色产生浅色调（tint）；加入黑色产生暗色调（shade）；加入灰色产生中间调（tone）。
| Colour Change 变化 | Ingredient Added 加入成分 |
|---|---|
| Tint (lighter) | + White |
| 浅色调 | + 白 |
| Shade (darker) | + Black |
| 暗色调 | + 黑 |
| Tone (softer/muted) | + Grey |
| 中间调（柔化/低沉） | + 灰 |
4. Perspective Rules: Vanishing Points | 透视法则：消失点
Linear perspective is the mathematical system for creating the illusion of depth on a flat surface. The core formula involves a horizon line (eye level) and one or more vanishing points (VPs) where parallel lines appear to converge.
线性透视是在二维平面上创造深度幻觉的数学系统。其核心公式涉及一条视平线（眼高水平线）和一个或多个消失点（VPs），平行线在此处看似汇聚。
One-Point Perspective: All receding parallel lines meet at a single vanishing point on the horizon. The formula is simple: draw your horizon line, place one VP, then radiate all depth lines from it.
一点透视：所有向后延伸的平行线都汇聚于视平线上的单一消失点。公式很简单：画出视平线，放置一个消失点，然后从该点辐射出所有深度线条。
Depth = Horizon Line + 1 Vanishing Point
深度 = 视平线 + 1 个消失点
Two-Point Perspective: Used for seeing an object's corner. Two vanishing points are placed on the horizon line, and edges recede to both. This formula handles most architectural drawings.
两点透视：用于呈现物体的转角。在视平线上放置两个消失点，物体的边缘分别向两边消失。这一公式适用于大多数建筑类素描。
Corner Depth = Horizon Line + 2 Vanishing Points
转角深度 = 视平线 + 2 个消失点
Atmospheric Perspective: A non-linear formula where distant objects appear lighter, bluer, and less detailed. It mimics the scattering of light by the atmosphere.
空气透视：一种非线透视公式，远处物体显得更浅、更蓝且细节更少，模拟了大气对光线的散射效果。
5. Human Figure Proportions | 人体比例定理
The human body follows classical proportional canons that artists have used for centuries. The most common formula uses the length of the head as the basic unit of measurement.
人体遵循经典的比修正典，几个世纪以来艺术家们一直沿用。最常见的比例公式以头部长度作为基本测量单位。
Ideal adult standing height ≈ 7.5 to 8 head lengths
理想成人站立身高 ≈ 7.5 至 8 个头长
Key proportion landmarks: The halfway point of the figure is at the groin/pubic bone. The elbows align with the waist, the wrists with the hips, and the fingertips reach mid-thigh. The eyes are positioned at the halfway point of the head vertically.
关键比例标记：人体的中心点位于腹股沟/耻骨处。肘关节与腰对齐，腕关节与髋部对齐，指尖达到大腿中部。眼睛位于头部垂直线的中点处。
When drawing a seated figure, the rule adjusts to roughly 5 to 6 head lengths, depending on posture. These constants allow you to maintain correct relationships in any pose.
画坐姿时，这一规则根据姿势调整为大约 5 至 6 个头长。这些常数让你能在任何姿态下保持正确的人体关系。
6. Tonal Value Scale | 明暗色调等级定理
Tonal value refers to the lightness or darkness of a colour or of a neutral grey. A standard value scale bridges pure white and pure black, and organising these steps is essential for realistic shading.
色调明度是指某种颜色或中性灰色的明暗程度。标准的色调等级在白和纯黑之间架起桥梁，掌握这些阶梯对于真实感的明暗表现至关重要。
A typical 9-step value scale formula:
一个典型的九级色调尺度公式：
| 1 White | 2 High Light | 3 Light | 4 Low Light | 5 Midtone | 6 High Dark | 7 Dark | 8 Low Dark | 9 Black |
| 1 白 | 2 高明度 | 3 亮 | 4 次亮 | 5 中间调 | 6 次暗 | 7 暗 | 8 低明度 | 9 黑 |
In a shaded sphere, the core zones are the highlight, light, halftone, core shadow, reflected light, and cast shadow. The transition from light to dark follows the formula: highlight gradually flows into halftone, then drops into the darkest zone at the core shadow, before picking up reflected light.
在一个着色球体中，核心区域包括高光、亮面、中间调、明暗交界线、反光和投影。从明到暗的过渡遵循这个公式：高光逐渐过渡到中间调，然后在明暗交界线处落入最暗区域，之后因反光再次提亮。
7. Composition: Rule of Thirds & Golden Ratio | 构图：三分法与黄金比例
Strong composition is often based on geometric 'formulas' that guide the viewer's eye. The two most important compositional theorems are the rule of thirds and the golden ratio.
有力的构图常常基于引导观者视线的几何“公式”。两个最重要的构图定理是三分法和黄金比例。
Rule of Thirds: Divide the canvas into a 3x3 grid using two equally spaced horizontal and two vertical lines. Placing the focal point at any intersection creates a more dynamic and interesting image than centring the subject.
三分法：用两条等距的水平线和两条垂直线将画面分成 3×3 的网格。将焦点放在任意交叉点上，比将主体置于中心更能创造出充满动感和趣味性的图像。
Focal Point = Grid Intersection (1/3, 2/3 lines)
焦点 = 网格交叉点（1/3、2/3 分割线）
Golden Ratio (φ ≈ 1.618): A proportion found throughout nature and classical art. The golden rectangle and golden spiral position elements along a graceful curve. Dividing a line so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part gives this divine proportion.
黄金比例（φ ≈ 1.618）：一种在自然界和古典艺术中随处可见的比例。黄金矩形和黄金螺旋使元素沿一条优美的曲线排列。将一条线段分割，使整体与较大部分的比值等于较大部分与较小部分的比值，就得到了这一神圣比例。
a/b = (a+b)/a = 1.618…
a/b = (a+b)/a = 1.618…
Leading lines, symmetry, and framing are other compositional tools, but they all stem from these underlying geometric rules.
引导线、对称性和框架构图是其他构图工具，但它们都源于这些基本的几何法则。
8. Shading Techniques & the Five-Tone System | 素描明暗技巧与五调子系统
Rendering form convincingly relies on observing how light falls on an object. The classic 'five-tone' shading formula provides a repeatable approach for any drawing.
逼真地表现形体依赖于观察光线如何落在物体上。经典的“五调子”明暗公式为任何素描提供了一种可重复的方法。
| Tone 调子 | Description 描述 | Location 位置 |
|---|---|---|
| 1. Highlight 高光 | The brightest point where light hits directly; usually left as white paper. | Light source side |
| 2. Light Grey 亮灰面 | Slightly darker than highlight, still receiving direct light. | Adjacent to highlight |
| 3. Core Shadow 明暗交界线 | The darkest part on the object where light transitions to shadow. | Between light and shadow |
| 4. Reflected Light 反光 | Light bouncing from surfaces nearby, making the shadow edge a bit lighter. | Shadow side, near bottom |
| 5. Cast Shadow 投影 | The shadow thrown by the object onto another surface; usually darkest and sharpest near the object. | Opposite light source |
The formulaic sequence is always: light, halftone, core shadow, reflected light, cast shadow. Mastering this order allows you to shade any simple form, from spheres to cylinders to complex folds of fabric.
这个公式化的顺序始终是：亮面、中间调、明暗交界线、反光、投影。掌握这一顺序，你就能为任何简单的形——从球体、圆柱体到复杂的布料褶皱——画出真实的明暗。
9. Colour Temperature & Emotional Formula | 色彩温度与情感公式
Colours are categorised as warm or cool, and this temperature directly influences the mood and spatial perception of an artwork. The psychological formula of colour affects how viewers interpret a piece.
色彩被分为暖色与冷色，这种温度感直接影响作品的情绪和空间感知。色彩的心理公式影响着观者对作品的理解。
Warm Colours: Red, Orange, Yellow. Formula effect: they appear to advance towards the viewer, energise a composition, and evoke feelings of warmth, passion, and excitement.
暖色：红、橙、黄。公式效应：它们看似向观看者靠近，为画面注入能量，唤起温暖、激情与兴奋的感受。
Cool Colours: Blue, Green, Violet. Formula effect: they recede into the background, create a calm or melancholic atmosphere, and suggest distance, freshness, or sadness.
冷色：蓝、绿、紫。公式效应：它们向背景退去，营造平静或忧郁的氛围，暗示距离、清新或悲伤。
A practical formula for depth: place warm tones in the foreground and cool tones in the background. This reinforces the illusion of space, as warm colours naturally pop forward while cool colours sink back.
一个实用的空间深度公式：将暖色调置于前景，冷色调置于背景。这强化了空间感，因为暖色自然向前突出，而冷色向后退去。
10. Texture Rendering Principles | 质感表现原理公式
Texture is the surface quality of an object, perceived through both touch and sight. Rendering it convincingly in art can be broken down into a few systematic approaches.
质感是物体表面的品质，通过触觉和视觉来感知。在艺术中逼真地表现质感可以归纳为几个系统化的方法。
The Highlight Formula: Smooth, shiny surfaces (glass, metal, polished wood) have sharp, bright highlights with distinct edges. Rough, matte surfaces (stone, fabric, skin) have soft, diffused highlights with blurred edges.
高光公式：光滑、闪亮的表面（玻璃、金属、抛光木材）具有边缘清晰、亮眼的高光。粗糙、无光泽的表面（石头、织物、皮肤）则具有柔和散射、边缘模糊的高光。
The Stroke Formula: Rendering texture heavily relies on the direction, length, and pressure of your marks. Use short, jagged strokes for rough bark; long, flowing, curved strokes for hair or water; and tight, cross-hatched lines for dense, coarse textures. The formula is to always follow the contour of the form while varying the stroke pattern for the specific material.
笔触公式：质感的表现很大程度上依赖于笔触的方向、长度与力度。粗糙树皮使用短而锯齿状的线条；头发或水使用悠长流动的曲线；紧密粗糙的纹理使用密的交叉排线。其公式是始终沿形体的轮廓走笔，同时根据具体材质变换笔触模式。
By combining the highlight rule with the stroke rule, you can simulate nearly any surface. Practice by methodically changing these two variables, and remember that observation is the true master formula behind all texture work.
将高光规则与笔触规则结合起来，你几乎能模拟出任何表面。通过有步骤地调整这两个变量进行练习，并记住：观察是所有质感表现背后真正的大师级公式。
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