📚 Year 10 CAIE Art: Formulas & Theorems Quick Reference Handbook | 艺术公式定理速查手册
This concise handbook brings together the essential formulas, theorems, and principles that every Year 10 CAIE Art student needs at their fingertips. From colour mixing equations to compositional geometry, these are the structural rules behind successful visual work — perfect for quick revision and coursework refinement.
这本精炼手册汇集了每一位Year 10 CAIE艺术学生都需要掌握的核心公式、定理与原理。从调色方程到构图几何，这些是成功视觉作品背后的结构性法则——非常适合快速复习和完善课程作业。
1. Colour Theory Fundamentals | 色彩理论基础
The three dimensions of colour are hue (the name of a colour), saturation (intensity or purity), and value (lightness or darkness). Every colour decision involves adjusting at least one of these properties.
色彩的三个维度是色相（颜色的名称）、饱和度（强度或纯度）和明度（明暗程度）。每一次色彩决策都涉及至少调整其中一个属性。
Primary colours in the traditional RYB model are red, yellow, and blue. They cannot be obtained by mixing, yet they form the basis of all other hues.
传统RYB模型中的原色是红、黄、蓝。它们无法通过混合获得，却是所有其他色相的基础。
Secondary colours are produced by mixing two primaries: orange (R+Y), green (Y+B), and violet (R+B).
二次色由两种原色混合而成：橙色（红+黄）、绿色（黄+蓝）和紫色（红+蓝）。
2. The Colour Wheel and Harmonies | 色环与配色和谐
A standard 12-segment colour wheel organises hues so that relationships become visible. Complementary pairs sit opposite each other and create maximum contrast.
标准的12段色环将色相组织起来，让关系变得直观可见。互补色对位于彼此对面，产生最大的对比度。
Analogous harmonies use three to five colours adjacent on the wheel; they produce a calm, unified feel with minimal tension.
类比和谐使用色环上相邻的三到五种颜色；它们营造出宁静统一的感觉，张力极小。
Triadic harmony selects three colours evenly spaced at 120° intervals — for example, red, yellow, and blue. This scheme offers vibrant balance.
三色和谐选择三个均匀间隔120°的颜色——例如红、黄、蓝。这种配色方案提供生动的平衡。
3. Tints, Shades and Saturation | 色调、阴影与饱和度
A tint is a colour mixed with white, increasing value and reducing saturation. A shade is a colour mixed with black, decreasing value. A tone is produced by adding grey, muting the saturation without drastically changing value.
色调（tint）是颜色与白色混合，提高明度并降低饱和度。阴影（shade）是颜色与黑色混合，降低明度。色调（tone）通过加入灰色获得，柔和饱和度而不大幅改变明度。
Saturation is measured as the distance from neutral grey. High-saturation colours appear vivid; low-saturation colours read as subtle, dusty, or atmospheric.
饱和度以距中性灰的距离来衡量。高饱和度的颜色显得鲜艳；低饱和度的颜色显得微妙、灰蒙或富有氛围感。
4. Warm vs Cool Colours | 暖色与冷色
Warm colours (red, orange, yellow) advance visually and are associated with energy, heat, and sunlight. Cool colours (blue, green, violet) tend to recede and evoke calm, shadow, or distance.
暖色（红、橙、黄）在视觉上前进，与能量、热量和阳光相关联。冷色（蓝、绿、紫）则趋于后退，引发平静、阴影或距离感。
The temperature of a colour is relative: a green that leans yellow feels warmer than a green that leans blue, even though green is generally cool.
颜色的温度是相对的：偏黄的绿色比偏蓝的绿色感觉更暖，尽管绿色通常属于冷色。
5. Perspective: One-Point and Two-Point | 透视：一点透视与两点透视
One-point perspective uses a single vanishing point on the horizon line. All parallel lines receding into space converge at this point; verticals remain vertical, horizontals remain horizontal.
一点透视在视平线上使用一个单一的消失点。所有向空间后方延伸的平行线汇聚于该点；竖直线保持垂直，水平线保持水平。
Two-point perspective employs two vanishing points on the horizon. Vertical edges stay straight up and down, but horizontal edges recede toward the left or right vanishing point, creating more dynamic spatial depth.
两点透视在视平线上使用两个消失点。垂直边保持竖直，但水平边分别向左或向右的消失点汇聚，创造出更具动态的空间深度。
6. The Golden Ratio and Rule of Thirds | 黄金比例与三分法
ximately 1.618. It is found in nature and classical art and is expressed as (a+b)/a = a/b.
黄金比例，通常用希腊字母φ（phi）表示，约为1.618。它存在于自然界和古典艺术中，表达式为(a+b)/a = a/b。
φ = (1 + √5) ÷ 2 ≈ 1.618
φ = (1 + √5) ÷ 2 ≈ 1.618
laced near the intersections of these lines tend to produce more engaging and balanced compositions than centering the subject.
三分法将画面划分为3×3网格。将焦点放在这些线条的交点附近，往往比将主体居中能产生更引人入胜且平衡的构图。
7. Figure Proportions: The 8-Head Canon | 人体比例：八头身法则
The idealised adult human figure is often drawn as approximately 8 heads tall. The head itself is used as the unit of measurement for the entire body.
理想化的成年人体通常被绘制为约8个头高。头部本身被用作整个身体的测量单位。
- Chin to nipple line ≈ 2 heads
- 下巴到乳头连线 ≈ 2个头长
- Nipple to navel ≈ 1 head
- 乳头到肚脐 ≈ 1个头长
- Navel to crotch ≈ 1 head
- 肚脐到裆部 ≈ 1个头长
- Head to crotch = 4 heads (midpoint of body)
- 头部到裆部 = 4个头长（身体的中点）
Arms extend so that fingertips reach mid-thigh; the elbow aligns with the waist. These proportional formulas provide a reliable foundation for figure drawing.
手臂伸展使指尖到达大腿中部；肘部与腰部对齐。这些比例公式为人物画提供了可靠的基础。
8. Compositional Balance and Hierarchy | 构图平衡与层次
Symmetrical balance places identical or very similar elements on either side of a vertical axis, creating formality and stability. Asymmetrical balance achieves equilibrium through contrasting yet visually equal weights, such as a large light shape balanced by a small dark one.
对称平衡在垂直轴两侧放置相同或非常相似的元素，营造出正式与稳定的感觉。不对称平衡则通过对比较强但视觉重量相等的元素达到均衡，比如一个大而浅的图形由一个深色小图形来平衡。
Visual hierarchy directs the viewer's eye through size, colour, contrast, and placement. The largest and highest-contrast element is typically read first.
视觉层次通过大小、颜色、对比度和位置引导观者的视线。最大且对比度最高的元素通常最先被注意到。
9. Texture and Mark-Making Techniques | 肌理与笔触技巧
Actual texture is the physical surface quality of the artwork; implied texture is the illusion of surface created through mark-making. Hatching, cross-hatching, stippling, and scumbling are foundational rendering techniques.
实际肌理是作品表面的物理质感；暗示性肌理是通过笔触创造的表面幻觉。排线、交叉排线、点画和薄涂是基础的渲染技法。
Consistent mark direction and pressure control both the perceived texture and the tonal value. Closely spaced marks read as darker; sparse marks read as lighter.
一致的笔触方向和力度控制着感知到的肌理和明暗调子。密集的笔触看起来较暗；稀疏的笔触看起来较亮。
10. Light and Shadow: Chiaroscuro | 光影：明暗对照法
Chiaroscuro is the treatment of light and shadow to model three-dimensional form. The five-value scale — highlight, light, midtone, shadow core, and cast shadow — provides a structured approach.
明暗对照法是通过光影处理来塑造三维形体。五阶调子——高光、亮部、中间调、阴影核心和投影——提供了一种结构化的方法。
The shadow core is the darkest part of the form shadow, located before the reflected light begins. Cast shadows are darkest nearest the object that blocks the light.
阴影核心是形体阴影中最暗的部分，位于反光开始之前。投影在靠近遮挡光的物体处最暗。
11. Principles of Design | 设计原则
Unity is achieved when all elements feel cohesive and belong together. Contrast draws attention through differences in colour, size, shape, or texture. Rhythm is created by repeating visual elements to generate movement.
统一感在所有元素感觉和谐且属于一体时实现。对比通过颜色、大小、形状或肌理的差异吸引注意力。韵律通过重复视觉元素来产生动感。
Proportion refers to the size relationship between parts and the whole; emphasis isolates one area as the focal point. These principles work together to strengthen visual communication.
比例指局部与整体之间的尺寸关系；强调则突出一块区域作为焦点。这些原则共同作用，以增强视觉传达。
12. Colour Mixing Formulas | 调色公式
Additive colour mixing uses light (RGB) and starts from black; subtractive mixing uses pigment (RYB/CMYK) and starts from white. In painting, subtractive rules apply.
加色混合使用光（RGB），从黑色开始；减色混合使用颜料（RYB/CMYK），从白色开始。在绘画中，适用减色规则。
Basic subtractive equations:
减色基本方程：
Red + Yellow = Orange
红 + 黄 = 橙
Yellow + Blue = Green
黄 + 蓝 = 绿
Red + Blue = Violet
红 + 蓝 = 紫
All three primaries mixed in roughly equal proportions produce a neutral dark, often called chromatic black. Adjusting the proportions shifts the bias toward brown or grey.
三种原色以大致相等的比例混合会产生中性深色，通常称为彩色黑。调整比例会使偏色偏向棕色或灰色。
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