📚 KS3 CAIE Art: Formula & Theorem Quick Reference Handbook | KS3 CAIE 艺术：公式定理速查手册
Art is often seen as a free and expressive subject, but behind every successful artwork lies a set of reliable principles, rules, and ‘formulas’ that help artists make informed decisions. This handbook brings together the essential formulas and theorems from the KS3 CAIE Art curriculum—covering colour, perspective, composition, shadow, proportion, and more. Think of this as your cheat sheet for building strong visual foundations, whether you are painting, drawing, or designing digitally.
艺术常被视为自由表达的学科，但在每一件成功的作品背后，都有一套可靠的原则、规则和“公式”帮助艺术家做出明智的决策。本手册汇集了 KS3 CAIE 艺术课程中必不可少的公式与定理，涵盖色彩、透视、构图、阴影、比例等领域。不论你是手绘、素描还是进行数字设计，都可以把它当作构建坚实视觉基础的速查表。
1. Colour Wheel Formula | 色轮公式
The 12-part colour wheel is built on a simple rule: primary colours (red, yellow, blue) are spaced evenly at 120° intervals; secondary colours (orange, green, violet) sit midway between primaries; tertiary colours fill the remaining gaps. This gives a formulaic way to predict harmonious colour schemes.
十二色色轮建立在一个简单的规则之上：三原色（红、黄、蓝）以 120° 的间隔均匀分布；二次色（橙、绿、紫）位于原色之间；三次色填补剩余空隙。这就提供了一种可以预测和谐配色的公式化方法。
Complementary colours are always opposite each other on the wheel: Red ↔ Green, Blue ↔ Orange, Yellow ↔ Violet. Using complements at full saturation creates maximum contrast, while mixing them in equal parts produces a neutral grey—an effect explained by subtractive colour mixing.
互补色在色轮上始终彼此相对：红 ↔ 绿，蓝 ↔ 橙，黄 ↔ 紫。以全饱和度使用互补色可产生最大对比度，而将它们等量混合则会产生中性灰色——这一效果可用减色混合来解释。
2. Tint, Shade and Tone Formula | 调色公式：色调、暗调与灰度
Tint = Pure Hue + White. Shade = Pure Hue + Black. Tone = Pure Hue + Grey (or both White and Black). This formula is vital for controlling value and mood. Adding white raises lightness and often creates a softer feel; adding black lowers lightness and can make colours feel heavier or moodier.
色调 = 纯色 + 白色。暗调 = 纯色 + 黑色。灰度调 = 纯色 + 灰色（或同时加白与黑）。这一公式对于控制明度和情绪至关重要。加白提高亮度，往往带来更柔和的感觉；加黑降低亮度，会让颜色显得更沉重或更有氛围感。
In KS3 projects, students are often asked to create a monochromatic colour scheme—by applying the tint/shade/tone formula systematically, you can produce a full value scale from light to dark using just one base hue.
在 KS3 课题中，学生经常被要求创作单色配色方案——系统地运用色调/暗调/灰度公式，你就能仅用一个基础色相，生成从亮到暗的完整明度梯度。
3. Basic Colour Harmony Rules | 基本色彩和谐法则
Analogous colours sit next to each other on the wheel (e.g., blue, blue-green, green). They create calm, unified compositions. Triadic harmony uses three colours equally spaced at 120° (e.g., red, yellow, blue), offering vibrant balance. Split-complementary takes one base colour and the two colours adjacent to its complement—this keeps contrast while reducing tension.
类似色在色轮上彼此相邻（如蓝、蓝绿、绿），它们营造出平静统一的构图。三角配色使用以 120° 等距分布的三种颜色（如红、黄、蓝），提供充满活力的平衡感。分裂互补色选取一种基色及其补色两侧的两种颜色——这样既保持了对比又降低了紧张感。
A practical formula: for a balanced composition, use a 70-20-10 ratio—70% dominant colour, 20% secondary colour, 10% accent. This interior design rule works equally well in paintings, posters, and sketchbook layouts.
一条实用公式：为了让构图平衡，可采用 70-20-10 的比例——70% 主色、20% 次要色、10% 点缀色。这条室内设计法则在绘画、海报和速写本排布中同样奏效。
4. One-Point Perspective Formula | 一点透视公式
Any scene with a single vanishing point on the horizon line follows this rule: all receding parallel lines converge to that vanishing point. The height of objects at a given distance can be calculated by drawing orthogonals from the object’s base and top to the vanishing point. This formula allows you to draw railway tracks, corridors, and building facades with realistic depth.
任何在天际线上只有一个消失点的场景都遵循这一规则：所有后退的平行线都汇聚到该消失点。通过从物体的底部和顶部向消失点引正交线，可以计算出物体在特定距离处的高度。运用这一公式，你可以画出具有真实纵深感的铁轨、走廊和建筑立面。
In CAIE Art at KS3, you are expected to apply this rule to freehand drawing, understanding that objects shrink proportionally as they get closer to the vanishing point—the mathematical basis is similar triangles, but the artistic focus is on visual consistency.
在 KS3 CAIE 艺术中，你需要将这一规则应用于徒手绘画，理解物体越靠近消失点按比例缩小的原理——其数学基础是相似三角形，但艺术的关注点在于视觉一致性。
5. Two-Point Perspective Formula | 两点透视公式
Two vanishing points are placed on the horizon line, usually beyond the picture plane. Vertical lines remain perfectly vertical. All horizontal lines recede to either the left or right vanishing point. This formula is essential for drawing objects at an angle, such as the corner of a building or a box rotated in space.
两个消失点位于天际线上，通常超出画面之外。垂直线始终保持完全垂直。所有水平线分别向左或向右消失点后退。这个公式对于绘制成角度的物体至关重要，比如建筑物的转角或在空间中旋转的箱体。
A common student error is placing both vanishing points too close together, which creates distorted, unnatural shapes. The formula works best when the vanishing points are far apart, often well beyond the edge of the paper.
学生常见的错误是把两个消失点放得太近，这会导致形状扭曲、不自然。当消失点相距较远——通常远远超出纸张边缘——时公式效果最佳。
6. Atmospheric Perspective Formula | 空气透视公式
Atmospheric perspective is governed by distance: as objects recede into the background, they become lighter in value, cooler in colour temperature, and less detailed. This happens because light scatters in the atmosphere, so distant mountains appear bluish and hazy. The formula can be remembered as: Distance ∝ (Value lightness) + (Colour coolness) + (Detail loss).
空气透视受距离支配：物体退入背景越远，其明度越亮、色温越冷、细节越少。这是因为光线在大气中散射，所以远山看起来发蓝且朦胧。这一公式可以记为：距离 ∝ （明度变亮） + （色温变冷） + （细节丢失）。
In KS3 landscape studies, applying this formula means foreground objects should be dark, warm, and highly textured, middle ground objects intermediate, and background the lightest, coolest, and simplest. This systematic layering creates instant depth.
在 KS3 风景画学习中，运用该公式意味着前景物体应暗、暖且纹理丰富，中景物体介于中间，背景则最亮、最冷、最简单。这种系统化分层能即刻营造出纵深感。
7. Golden Ratio (φ) and Rule of Thirds | 黄金比例（φ）与三分法则
The Golden Ratio φ ≈ 1.618. A line is divided so that the whole length divided by the longer part equals the longer part divided by the shorter part. In art, the Golden Rectangle (ratio 1:1.618) is considered aesthetically pleasing. The Rule of Thirds is a simplified approximation: divide the image into nine equal parts with two horizontal and two vertical lines; place focal points at the intersections.
黄金比例 φ ≈ 1.618。一条线段被分割，使得全长除以较长部分等于较长部分除以较短部分。在艺术中，黄金矩形（比例 1:1.618）被认为具有美感。三分法则是一个简化的近似：用两条水平线和两条垂直线将画面分成九个等份，将焦点放在交叉点上。
For KS3 compositions, the Rule of Thirds is often more accessible. The formula: key elements (eyes in a portrait, horizon line, main tree) should sit on or near the ⅓ or ⅔ divisions rather than in the centre, unless symmetry is intentional.
对于 KS3 构图，三分法则通常更易上手。公式：关键元素（肖像中的眼睛、天际线、主要树木）应位于或靠近三分之一或三分之二分割处，而不是画面正中央，除非有意追求对称。
8. The Light and Shadow Formula | 光与影公式
For a single light source, the division of light and dark follows a repeatable pattern: highlight, lit area, core shadow, reflected light, and cast shadow. The formula states that the core shadow sits at the point where the surface curves away from the light and is typically the darkest part of the form, darker even than the cast shadow. Reflected light within the shadow is never as bright as the directly lit area.
对于单一光源，亮部与暗部的划分遵循一个可重复的模式：高光、受光面、明暗交界线、反光和投影。该公式指出，明暗交界线位于物体表面背离光源的转折处，通常是形体上最暗的部分，甚至比投影还暗。阴影内的反光永远不会比直接受光面更亮。
This model is fundamental to shading spheres, cubes, and cylinders. Practice the formula by drawing an egg under a desk lamp: identify all five zones. Measuring angles of light rays can be approximated by treating the light source as a point and projecting lines tangentially onto the object.
这一模型是绘制球体、立方体和圆柱体明暗的基础。通过在一盏台灯下画一个鸡蛋来练习这个公式：识别出所有五个区域。测量光线角度可以近似地将光源视为一个点，并将光线切线投射到物体上。
9. Facial Proportion Formulas | 面部比例公式
In portrait drawing, the ‘classical’ proportions serve as a reliable formula: the eyes are positioned halfway between the top of the skull and the chin. The face can be divided into three equal sections: hairline to eyebrows, eyebrows to nose base, nose base to chin. The width of the head is roughly five eye-widths across, with the space between the eyes being equal to one eye-width.
在肖像画中，“古典”比例是一套可靠的公式：眼睛位于头顶到下巴的正中间。面部可分为三个相等的部分：发际线到眉毛、眉毛到鼻底、鼻底到下巴。头部的宽度大约是五个眼睛的宽度，两眼之间的距离等于一只眼睛的宽度。
While real faces vary, using this formula as a starting point prevents major anatomy errors. KS3 students should measure these proportional relationships on reference images and lightly mark them before drawing details.
虽然真实面孔各有差异，但以此公式为起点可以防止重大的解剖错误。KS3 学生应该在参考图片上测量这些比例关系，并在绘制细节之前轻轻标出。
10. The Rule of Similitude in Texture and Pattern | 纹理与图案的相似性法则
When creating a unified artwork, patterns and textures should obey a principle of ‘similitude’: repeating elements should vary slightly in size, orientation, or spacing according to surface curvature or perspective. The formula: the perceived frequency of a pattern increases as it recedes into depth, and the individual marks become smaller.
在创作统一的作品时，图案和纹理应遵循“相似性”原则：重复元素的大小、方向或间距应根据表面曲度或透视而略微变化。公式是：随着图案向深处后退，其视觉频率增加，单个标记变小。
This mathematical shrinking can be achieved by eye or by using a perspective grid. In observational drawing, counting the number of leaves or bricks visible at different depths helps artists apply this formula accurately.
这种数学性的缩小可以通过肉眼或使用透视网格来实现。在观察性绘画中，数一数不同深度处可见的树叶或砖块数量，有助于艺术家准确地运用这一公式。
11. The Formula of Emphasis through Contrast | 通过对比突出重点的公式
Any element that deviates from a pattern becomes a focal point. The formula for emphasis: contrast in any visual dimension—size, shape, colour, value, texture, direction, position—draws the eye. The strongest emphasis occurs when multiple types of contrast converge on the same spot.
任何偏离模式的元素都会成为焦点。突出重点的公式是：在任何视觉维度上的对比——大小、形状、颜色、明度、纹理、方向、位置——都能吸引视线。当多种对比汇聚在同一点时，重点最为强烈。
Use a contrast hierarchy: a small red circle in a field of large blue squares will dominate. In CAIE KS3 projects, plan your focal point first, then orchestrate surrounding elements to support it through lowered contrast.
利用对比层级：在一片蓝色大方块中放入一个红色小圆，该圆会成为视觉主导。在 CAIE KS3 课题中，先规划好你的焦点，然后通过降低周围元素的对比度来烘托它。
12. Colour Value to Grayscale Conversion | 色彩明度转灰阶公式
While digital tools can instantly convert colour to grayscale, artists need a mental formula. Approximate value can be estimated using the weighted luminance: Luminance = 0.3×Red + 0.59×Green + 0.11×Blue (in RGB terms). In painting terms, yellow typically has a high value, blue has a low value, and pure red and green sit in the middle range.
虽然数字工具可以瞬间将色彩转为灰阶，但艺术家需要一条心理公式。近似的明度可以通过加权亮度来估算：亮度 = 0.3×红 + 0.59×绿 + 0.11×蓝（以 RGB 值计）。在绘画术语中，黄色通常明度较高，蓝色明度较低，纯红和纯绿处于中明度范围。
Why is this formula important? If two colours have the same value, they blend together when reproduced in black and white, losing contrast. Skilful artists check value by squinting: the eye sees luminance more easily when shapes are blurred. This ensures the tonal structure of the artwork holds.
为什么这条公式很重要？如果两种颜色明度相同，在黑白再现时它们会融为一体，失去对比。熟练的艺术家通过眯眼来检查明度：当形状变得模糊时，眼睛更容易看出亮度差异。这能确保作品的调性结构稳固。
Published by TutorHao | Art Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导