📚 Year 10 OCR Art: Formula & Theorem Quick Reference Handbook | 10年级 OCR 艺术：公式定理速查手册
Art may seem like pure intuition, but behind every successful composition lies a set of visual 'formulas' and principles that guide the eye. This quick reference handbook brings together the essential theorems of colour, perspective, proportion and design taught in the Year 10 OCR Art course — from the mathematics of the golden ratio to the spatial logic of one-point perspective. Each entry follows a concise 'rule-thumb' format so you can absorb and apply it directly to your own creative explorations.
艺术看似全凭直觉，然而每一幅成功的作品背后都有一套引导视线的视觉“公式”与原理。这本速查手册汇集了 10 年级 OCR 艺术课程中色彩、透视、比例和设计的核心定理——从黄金比例的数学规律到一点透视的空间逻辑。每个条目都采用简明的“经验法则”格式，方便你吸收并直接运用到自己的创意探索中。
1. The Colour Wheel and Harmony Equations | 色轮与色彩和谐方程
The traditional 12-part colour wheel is built from three primaries (red, yellow, blue), three secondaries (orange, green, violet) and six tertiaries (mixes of a primary with a neighbouring secondary). Harmony 'equations' select colours according to their geometric relationship on the wheel. Complementary colours sit opposite each other and produce maximum contrast. Analogous colours are next to each other and create calm, unified schemes. A triadic harmony uses three colours equally spaced like an equilateral triangle, while split-complementary takes one colour plus the two neighbours of its complement.
传统的 12 色色轮由三原色（红、黄、蓝）、三间色（橙、绿、紫）和六复色（原色与相邻间色的混合）构成。和谐“方程”根据色彩在色轮上的几何关系进行选取。互补色彼此相对，产生最大对比度；类似色彼此相邻，营造宁静统一的配色。三色组和谐采用等边三角形分布的三种颜色，而分裂互补色则选择一种颜色及其互补色两侧的两种颜色。
- Complementary pair: Red + Green; Blue + Orange; Yellow + Violet
- 补色对： 红 + 绿；蓝 + 橙；黄 + 紫
- Triadic example: Red, Yellow, Blue (primaries) or Orange, Green, Violet (secondaries)
- 三色组示例： 红、黄、蓝（原色）或橙、绿、紫（间色）
2. HSL: The Colour Attribute Formula | HSL：色彩属性公式
Every colour can be described by three coordinates: hue (the position on the colour wheel in degrees), saturation (intensity or purity of the colour) and lightness (how light or dark the colour is). In paint, you modify lightness with white (creating tints) or black (creating shades), and desaturate by mixing with its complement, which produces tones.
每种颜色都可用三个坐标来描述：色相（在色轮上的角度位置）、饱和度（色彩的强度或纯度）和明度（颜色的明暗程度）。在颜料中，你可以通过加入白色来改变明度（产生浅色），加入黑色产生暗色，并通过混合补色来降低饱和度，从而产生灰色调。
+ White, Shade = Hue + Black, Tone = Hue + Grey (or complement)
浅色 = 色相 + 白， 暗色 = 色相 + 黑， 灰色调 = 色相 + 灰（或补色）
3. Additive and Subtractive Colour Mixing | 加色混合与减色混合
al screens. Subtractive mixing (CMY/CMYK), used in painting and printing, works by absorbing (subtracting) wavelengths. Cyan, Magenta and Yellow are the primaries; mixing all three produces a dark neutral, hence the addition of Key (black) in inks.
加色混合（RGB）是光的行为：红 + 绿 = 黄；绿 + 蓝 = 青；红 + 蓝 = 品红；三者全亮 = 白。这适用于数字屏幕。减色混合（CMY/CMYK）用于绘画和印刷，通过吸收（减去）波长来工作。青、品红和黄是三原色；三者混合产生暗中性色，因此油墨中引入黑色（Key）作为第四色。
Pigment primaries: Cyan + Magenta + Yellow → Black (muddy)
颜料三原色：青 + 品红 + 黄 → 黑（浑浊）
4. The Golden Ratio and the Rule of Thirds | 黄金比例与三分法则
ature and classical art as a formula for pleasing proportions. Divide a line so that the whole length is to the longer part as the longer part is to the shorter. The rule of thirds is a simplified framing guide: place key elements along the lines or at the intersections of a grid divided into nine equal rectangles. The eye naturally gravitates to these power points, creating dynamic balance without static centrality.
黄金比例 φ ≈ 1.618 作为悦目比例的公式，出现在自然与古典艺术中。将一条线段分割，使整体与较长部分的比值等于较长部分与较短部分的比值。三分法则是一个简化的构图指引：将画面用两横两竖分成九个相等矩形，将关键元素放在线条或交点（力量点）上。视线自然被这些力量点吸引，避免了死板的中心对称，营造出动态平衡。
Golden ratio: a/b = (a+b)/a ≈ 1.618
5. Linear Perspective Theorems: One, Two and Three Points | 线性透视定理：一点、两点和三点透视
One-point perspective uses a single vanishing point on the horizon line; all depth lines converge there. This creates a strong sense of a frontal view, like a railway track disappearing in the distance. Two-point perspective employs two vanishing points on the horizon, making objects look dynamic and angled — ideal for drawing buildings from a corner. Three-point perspective adds a third vanishing point far above or below, exaggerating height or depth as in a skyscraper seen from the ground.
一点透视在地平线上使用单一消失点，所有深度线都向该点汇聚。这营造了强烈的正面视觉效果，就像消失在远方的铁轨。两点透视在地平线上使用两个消失点，使物体呈现出富有动感的斜角——非常适合从转角处绘制建筑。三点透视在地平线上方或下方增加第三个消失点，夸张高度或深度，例如从地面仰望摩天大楼。
| 1-point: Frontal, tunnel-like, 1 VP on horizon | 一点： 正面、隧道感，地平线上 1 个消失点 |
| 2-point: Angled, 2 VPs on horizon | 两点： 带角度，地平线上 2 个消失点 |
| 3-point: Dramatic height/depth, 2 VPs on horizon + 1 above/below | 三点： 戏剧性的高度/深度，地平线上 2 点 + 上方或下方 1 点 |
6. Atmospheric Perspective: The Distance Formula | 大气透视：距离公式
As objects recede into the distance, they lose contrast, saturation and detail, and shift towards the colour of the atmosphere (usually pale blue or grey). This 'formula' lets artists simulate depth without strict linear construction. In practice, foreground elements are darkest and most detailed; middle ground has mid-contrast; background is faint, cooler and hazy. Overlap, size reduction and position on the picture plane reinforce the illusion.
物体向远处退缩时，其对比度、饱和度和细节会逐渐降低，并趋近于大气的色彩（通常为浅蓝或灰色）。这一“公式”让艺术家无需严格的线性构造就能模拟深度。实践中，前景元素最暗、细节最丰富；中景为中等对比度；背景则淡雅、偏冷、朦胧。叠加、尺寸缩小和画面位置进一步增强了空间幻觉。
- Foreground: sharp, dark, warm, high detail
- 前景： 清晰、暗、暖、细节丰富
- Midground: moderate contrast, some detail
- 中景： 中等对比度，部分细节
- Background: soft, light, cool, blurred
- 背景： 柔和、亮、冷色、模糊
7. Human Proportions: Vitruvian Man and the 8-Head Canon | 人体比例：维特鲁威人与 8 头身法则
Leonardo da Vinci's Vitruvian Man illustrates ideal proportions: height equals arm span, the navel is the centre of the circle, the head is 1/8 of the total height. The 8-head canon is a formula used by figurative artists: the pubis is at mid-height; knees are quarter-height from the ground; the elbow aligns with the waist; and the hand measures about the face length.
达芬奇的《维特鲁威人》展示了理想比例：身高等于臂展，肚脐为圆的中心，头部占总高度的 1/8。8 头身法则是具象艺术家使用的公式：耻骨位于一半身高处；膝盖距地面四分之一身高；肘部与腰齐平；手的长度约等于面部长度。
Total body height = 8 × head length
全身高度 = 8 × 头长
For the face, the 'rule of fifths' and 'three divisions' apply: eyes sit halfway down the head; the face divides horizontally into three equal sections — hairline to brow, brow to nose base, nose base to chin. The width is approximately five eye-widths.
对脸部而言，“五眼法”和“三庭法”适用：眼睛位于头部高度的中间；面部在水平方向分为三等份——发际线至眉、眉至鼻底、鼻底至下巴。面部宽度约等于五个眼睛的宽度。
8. Design Principle Equations: Balance, Contrast and Emphasis | 设计原理方程：平衡、对比和强调
ces different elements in asymmetric balance (e.g., a large light shape counterbalanced by a small dark shape). Contrast is the ratio of difference between elements — = 40:60. Emphasis is the anomaly that breaks a predictable pattern, drawing the eye first.
视觉平衡可理解为一个等式：对称平衡中，左侧的视觉总重量与右侧相等；不对称平衡中，不同元素相互抵消（如大面积浅色形状与小面积深色形状相平衡）。对比是元素间差异的比率——高对比 ≈ 明暗比 90:10；低对比 ≈ 40:60。强调是打破可预测模式的异常元素，首先吸引目光。
- Symmetrical balance: mirror-image stability
- 对称平衡： 镜像般的稳定感
- Asymmetrical balance: unequal parts that still feel stable
- 不对称平衡： 各部分不等但整体仍显稳定
- Radial balance: elements arranged around a central point
- 放射平衡： 元素围绕中心点排列
9. Gestalt Laws of Perception | 格式塔感知定律
Gestalt principles describe how the human brain organises visual information into wholes. Proximity: objects close together are seen as a group. Similarity: like elements (shape, colour, size) belong together. Closure: the mind fills missing gaps to see a complete shape. Continuity: the eye follows smooth paths. Figure-ground: we separate the main subject (figure) from its surroundings (ground).
格式塔原理描述了人脑如何将视觉信息组织成整体。接近性：彼此靠近的对象被视为一组。相似性：相似元素（形状、色彩、大小）被认为是一体的。闭合性：大脑会填补缺失部分以看见完整形状。连续性：视线会沿平滑路径移动。图底关系：我们将主体（图）与其周围环境（底）分离开来。
Gestalt mantra: 'The whole is other than the sum of its parts.'
格式塔箴言：“整体大于部分之和。”
10. Tonal Value: The Five-Tone Formula | 色调值：五调公式
To give a form three-dimensional volume, artists apply a tonal value scheme. The classic division includes highlight, half-tone (the true local colour), core shadow (the darkest part on the form itself), reflected light (bounced from surrounding surfaces) and cast shadow (the shadow thrown onto another surface). The transition from light to dark is not arbitrary; it follows the shape’s contour and the light source's direction.
为了赋予形体三维立体感，艺术家应用一套色调值方案。经典分法包括高光、中间调（物体固有颜色）、明暗交界线（形体自身最暗的部分）、反光（周围表面反射的光线）和投影（投在其他表面上的影子）。明暗的过渡并非随意，而是遵循形体的轮廓与光源的方向。
- Highlight: directly hit by light
- 高光： 光线直射处
- Half-tone: true colour, angled to light
- 中间调： 物体固有色，与光源成角度
- Core shadow: the darkest area on the object
- 明暗交界线： 物体上最暗区域
- Reflected light: soft light bouncing from nearby surfaces
- 反光： 从附近表面反射的柔和光线
- Cast shadow: sharp-edged shadow on another surface
- 投影： 投落在其他表面上的锐利阴影
11. Visual Weight and the Balance Calculation | 视觉重量与平衡计算
ness of an element. Dark colours feel heavier than light ones; large shapes outweigh small ones; high contrast and complex textures carry more weight than smooth, low-contrast areas. To check balance, imagine a fulcrum at the centre of the composition: the 'moment' uld roughly equalise. This explains why a small intense red shape can balance a large neutral blue area.
视觉重量是元素被感知到的重量。深色比浅色感觉更重；大形状重于小形状；高对比和复杂纹理比平滑、低对比区域更具重量感。检查平衡时，可想象在构图中心有一个支点：“力矩”（重量 × 距支点距离）应大致相等。这就解释了为什么一个强烈的红色小形状能平衡一大片中性蓝色区域。
| Factor | Increases weight |
| 因素 | 增加重量 |
| Colour value | Darker, more saturated |
| 色彩明度 | 更深、更饱和 |
| Size | Larger |
| 尺寸 | 更大 |
| Texture | Complex, rough |
| 纹理 | 复杂、粗糙 |
| Position | Farther from centre (leverage) |
| 位置 | 离中心越远（杠杆效应） |
12. Pattern, Rhythm and Movement | 图案、节奏与动势
A pattern is the repetition of an element — shape, line or colour — ontrolled through dynamic lines: diagonals suggest action; curves lead the eye gently; zigzags create tension. The formula 'Repetition + Variation = Rhythm' helps turn a static design into a visual journey.
图案是某种元素（形状、线条或色彩）在面上的重复。节奏是通过带有变化的重复所创造出的有序动感，很像音乐的节拍。视觉动势可通过动态线条来控制：斜线暗示行动；曲线温柔地引导视线；折线则制造张力。公式“重复 + 变化 = 节奏”有助于将静态设计转变为一场视觉之旅。
- Regular rhythm: equal spacing and identical elements
- 规则节奏： 等距且相同的元素
- Flowing rhythm: undulating, organic repetitions
- 流动节奏： 起伏的、有机的重复
- Progressive rhythm: elements change gradually in size or colour
- 渐进节奏： 元素在大小或色彩上逐渐变化
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