📚 Year 9 SQA Art: Quick-Reference Handbook of Formulas & Theorems | Year 9 SQA 艺术：公式定理速查手册
Art may seem a realm of free expression, but powerful images often rely on predictable visual principles — much like formulas and theorems in science. This handbook collects the essential 'equations' of art for Year 9 SQA students: colour mixing, proportion systems, perspective geometry and design rules. Use these quick references to analyse artworks and strengthen your own compositions.
艺术看似自由表达的领域，但富有感染力的图像常依赖于可预见的视觉原理——就像科学中的公式和定理。这本手册收集了面向 SQA 九年级学生的艺术核心“公式”：色彩混合、比例系统、透视几何和设计法则。借助这些速查要点，你能分析艺术作品并增强自己的构图能力。
1. The Colour Wheel Formula | 色轮公式
The 12-part colour wheel is built from three primary colours: red, yellow and blue. Think of them as the 'elemental colours' that cannot be created by mixing.
12 色色轮由三种原色构建：红、黄、蓝。可将它们视为无法通过混合获得的“元素色”。
ry colour. Red + yellow = orange, yellow + blue = green, and blue + red = violet (purple).
等量混合两种原色生成间色。红 + 黄 = 橙，黄 + 蓝 = 绿，蓝 + 红 = 紫（紫罗兰）。
When a primary is mixed with its adjacent secondary, you obtain a tertiary colour, such as red-orange or blue-green. The wheel thus offers 12 precise hues arranged by chromatic steps.
当原色与相邻间色混合时，便得到三次色，如红橙或蓝绿。色轮由此以色彩阶步排列出 12 种精确色相。
Primary + Primary = Secondary; Primary + Secondary = Tertiary
原色 + 原色 = 间色；原色 + 间色 = 三次色
| Primary | + | Primary | = Secondary |
|---|---|---|---|
| Red (红) | + | Yellow (黄) | Orange (橙) |
| Yellow (黄) | + | Blue (蓝) | Green (绿) |
| Blue (蓝) | + | Red (红) | Violet (紫) |
2. Complementary Contrast Theorem | 补色对比定理
Colours directly opposite each other on the colour wheel are complements. The three classic complementary pairs are red and green, blue and orange, yellow and violet.
色轮上正对的颜色互为补色。三对经典补色是红与绿、蓝与橙、黄与紫。
When placed side by side, complementary colours intensify each other — their contrast creates maximum visual vibration. Mixing true complements, however, neutralises them into a grey or brown.
补色并置时会相互强化——其对比产生最强的视觉振动。然而，将纯正的补色混合则会中和，生成灰色或棕色。
This theorem is crucial for creating focal points and balancing vibrant compositions. Use it to make a subject pop or to tone down overly bright areas.
该定理对于创造视觉焦点和平衡鲜活跃动的构图至关重要。可用它让主体跃出画面，或弱化过亮的区域。
Complementary pairs: R ↔ G, B ↔ O, Y ↔ V
补色对：红 ↔ 绿，蓝 ↔ 橙，黄 ↔ 紫
3. Golden Ratio in Composition | 构图黄金比例
The golden ratio, often denoted by the Greek letter φ (phi), appears in nature and classical art. Its approximate value is 1.618. A rectangle built with sides in the ratio 1 : 1.618 is considered especially harmonious.
黄金比例常用希腊字母 φ（斐）表示，存在于自然与古典艺术中。其近似值为 1.618。边长为 1 : 1.618 的矩形被认为格外和谐。
To apply this in a composition, place key elements along a golden spiral or divide your canvas into golden sections. Many artists position the horizon at the golden mean rather than exactly in the centre.
在构图中应用时，可将关键元素沿黄金螺旋安置，或将画面按黄金比例分割。许多画家将地平线放在黄金分割处，而非正中间。
φ = (1+√5) ÷ 2 ≈ 1.618
φ = (1+√5) ÷ 2 ≈ 1.618
When drawing a portrait, you can use the golden ratio to position the eyes: they often sit approximately halfway down the head, but the distance from the chin to the eyes relates to the overall head height in a pleasing proportion close to φ.
绘制肖像时，可利用黄金比例定位眼睛：双眼大致位于头部一半处，但从下巴到眼睛的距离与头部总高的比例往往接近 φ，令人悦目。
4. Rule of Thirds Grid | 三分法则网格
The rule of thirds is a simplified compositional formula. Divide your picture plane into nine equal rectangles by drawing two equally spaced horizontal lines and two equally spaced vertical lines.
三分法则是一种简化的构图公式。用两条等距水平线和两条等距垂直线将画面分为九个相等的矩形。
Place the subject or focal point at one of the four intersections. This off-centre placement tends to create more dynamic tension than centring everything.
将主体或焦点放在四个交叉点之一上。这种偏离中心的布置往往比所有元素居中更能营造出动感张力。
Horizons can be aligned with the upper or lower third line, depending on whether you wish to emphasise sky or land. The grid is a quick way to check balance.
地平线可根据你想强调天空还是大地而对准上三分之一或下三分之一线。该网格是快速检查平衡的工具。
| Grid Rule | Effect |
|---|---|
| Subject on intersection | Dynamic focus |
| Horizon on lower third | Emphasises sky |
| Horizon on upper third | Emphasises land |
画面宽 × 1/3 ≈ 交叉线位置
5. One-Point Perspective Equation | 一点透视方程
One-point perspective uses a single vanishing point on the horizon line. All receding parallel lines (orthogonals) converge at that point. It is ideal for corridors, roads or railway tracks viewed straight on.
一点透视在地平线上使用单一的消失点。所有后退的平行线（正交线）都汇聚于该点。它非常适合表现正视的走廊、道路或铁轨。
The basic formula: draw a horizontal horizon line, mark a vanishing point (VP) at its centre. Frontal planes remain undistorted; depth lines radiate from VP.
基本公式：画一条水平地平线，在其中央标出消失点（VP）。正面平面保持不变形；纵深线从 VP 放射而出。
Objects equally spaced in depth appear to converge. The spacing compresses according to a simple projection rule: each successive unit is drawn smaller and closer together as it nears VP.
等距排列的物体在纵深方向显得汇聚。间距按简单的投影规则压缩：每向后一个单元，越接近 VP 则绘制得越小、越密。
Depth scaling: size ∝ 1 / distance from VP
深度缩放：尺寸 ∝ 1 / 距VP的距离
6. Two-Point Perspective Vanishing Points | 两点透视消失点
Two-point perspective uses two vanishing points placed on the horizon line, typically far apart. Vertical edges remain parallel and vertical; only horizontal edges recede towards VP1 or VP2.
两点透视在地平线上使用两个通常相距甚远的消失点。垂直边仍保持平行和竖直；只有水平边向 VP1 或 VP2 后退。
This formula is applied when you view a corner of a building or a box. The angle between the receding planes determines the positions of the vanishing points.
当你观看建筑物或方盒的转角时，应用此公式。后退平面之间的角度决定了消失点的位置。
To construct a cube, draw the nearest vertical edge, then project its top and bottom towards both VPs. The back edges are determined by the intersection of sightlines.
要构建立方体，先画出最近的垂直边，然后将其上下端点向两个 VP 投射。后部边缘由视线交点确定。
VP₁ ← object corner → VP₂
VP₁ ← 物体转角 → VP₂
7. Value Scale Formula | 明度阶梯公式
A value scale organises tones from pure white to pure black in even steps. A typical 9-step scale labels white as value 10 and black as value 1, with medium grey around value 5.
明度阶梯将色调从纯白到纯黑按均匀梯级排列。典型的 9 级阶梯将白标为明度 10，黑标为 1，中灰约为 5。
Mixing formula: start with white, then incrementally add exactly measured amounts of black to create a sequence of middle greys. Each step should reflect an equal perceptual jump in lightness.
混合公式：从白色开始，然后逐步加入精确计量的黑色，创造出一系列中灰。每一步应体现出相等的明度感知跳跃。
High-key compositions use values 7–10; low-key works concentrate on 1–4. A full range of value (1–10) creates the strongest illusion of volume and light.
高调构图使用明度 7–10；低调作品集中在 1–4。全范围明度（1–10）能营造最强的体积与光感错觉。
Step n: Grey_n = White - (n × black increment), n = 1 to 9
第 n 级：灰度_n = 白 - (n × 黑色增量)，n = 1 至 9
8. Colour Harmony Rules | 色彩和谐法则
Harmonious colour schemes follow geometric relationships on the colour wheel. The most common formulas are analogous, triadic and split-complementary.
和谐配色遵循色轮上的几何关系。最常用的公式是类似色、三角色和分裂补色。
An analogous scheme uses three adjacent hues (e.g., blue, blue-green, green) and creates serene, cohesive designs. The triadic formula selects three colours evenly spaced by 120° (e.g., red, yellow, blue), offering vibrant contrast while maintaining balance.
类似色方案使用三个相邻色相（如蓝、蓝绿、绿），营造宁静统一的设计。三角色公式选择彼此间隔 120° 的三种颜色（如红、黄、蓝），在保持平衡的同时提供鲜艳对比。
Split-complementary harmony modifies the stark complementary pair: instead of using the direct opposite, it uses the two neighbours of the complement (e.g., red with yellow-green and blue-green). This softens contrast while retaining high energy.
分裂补色和声弱化了鲜明的补色对：它不使用直接对立色，而是用补色的两个相邻色（如红与黄绿和蓝绿）。这柔化了对比，同时保持高能量。
Triadic angle = 360° ÷ 3 = 120°
三角色夹角 = 360° ÷ 3 = 120°
9. Balance and Symmetry Principles | 平衡与对称原理
Visual balance is the distribution of visual weight in a composition. Symmetrical balance (formal balance) mirrors elements across a central axis — a formula that conveys stability and order.
视觉平衡是构图中视觉重量的分配。对称平衡（形式平衡）围绕中轴线镜像元素——这是一种传递稳定与秩序的公式。
Asymmetrical balance uses dissimilar objects to offset each other, like a large pale shape balanced by a small dark one. The 'equation' here is not about identical shapes but about equal visual weight.
非对称平衡用不相同的物体相互抵消，例如一个大的浅色形状被一个小的深色形状平衡。此处的“等式”不在于相同形状，而在于相等的视觉重量。
Radial symmetry springs from a central point, with elements arranged in a circular pattern. This formula is common in mandalas, rose windows and natural forms.
辐射对称源自一个中心点，元素以圆形模式排列。该公式常见于曼荼罗、玫瑰窗和自然形态中。
Visual weight = f (size, colour saturation, contrast, texture)
视觉重量 = f (尺寸, 色彩饱和度, 对比度, 肌理)
10. Proportions of the Human Figure | 人体比例标准
For centuries, artists have used a measurement system to depict the human body. A classic canon divides an adult standing figure into 7.5 to 8 head lengths. The halfway point typically falls at the hip joint.
几个世纪以来，艺术家们一直使用测量系统描绘人体。经典准绳将成人立姿分为 7.5 至 8 个头长。中点通常落在髋关节处。
The eyes sit halfway down the head; the shoulders measure roughly two head widths across. The elbows align with the waist, and the fingertips reach about mid-thigh.
眼睛位于头部一半高度处；肩宽约为两个头宽。肘部与腰部齐平，指尖大约触及大腿中部。
These proportional formulas ensure consistency, whether sketching from observation or imagination. Even stylised characters often adhere to a modified head-count ratio.
这些比例公式无论对观察写生还是想象作画都能确保一致性。即便风格化的角色通常也遵循修改后的头数比例。
Figure height = 7.5 × head length
人体身高 = 7.5 × 头长
11. Line Quality and Expression | 线条质感与表现
Line is more than outline — it can convey motion, weight and emotion through variations in thickness, pressure and speed. Thick, dark lines feel heavy and assertive; thin, light lines suggest delicacy and distance.
线条不仅是轮廓——通过粗细、压力与速度的变化，线条能传达运动感、重量与情感。粗深线条感觉沉重而肯定；细浅线条暗示柔美与距离。
A single continuous line can describe form, but varied line weight ('lost and found' edges) adds life. The formula: use heavier lines in shadow areas and where forms overlap, lighter lines on illuminated edges.
单根连续线可以描绘形体，但变化的线重（“虚实”边缘）更添生气。其公式为：阴影区域及形体交叠处使用较重的线，受光边缘使用较淡的线。
Gesture drawing relies on swift, flowing lines to capture action. Think of a line's speed as part of the equation: a quickly drawn line carries kinetic energy, while a slow, studied line offers calm precision.
动态速写依赖快速流畅的线条捕捉动作。可将线条速度视为方程的一部分：快速绘制的线条携带动能，而缓慢刻画的线条提供沉稳的精确度。
Line energy ∝ speed × pressure
线条能量 ∝ 速度 × 压力
12. Shading and Light Logic | 明暗与光影逻辑
Logical shading follows the direction and intensity of a light source. The five-tone formula for rendering a sphere includes highlight, light tone, mid-tone, core shadow and reflected light.
合乎逻辑的明暗应遵循光源的方向和强度。渲染球体的五调子公式包括高光、亮部、中间调、明暗交界线（核心阴影）和反光。
Place the core shadow along the edge where the form turns away from the light — it is the darkest area and is not the edge of the object itself. Reflected light, slightly lighter, appears on the opposite side due to bounce light from surroundings.
将明暗交界线置于形体背离光源的转折边缘处——它是最暗的区域，并非物体的边缘本身。反光稍亮，因四周反射光而出现在另一侧。
Cast shadows obey a projection formula: the shadow's length and angle result from the light source's height and direction. Low light produces long shadows; high light shortens them.
投影遵循投射公式：阴影的长度和角度由光源的高度和方向决定。低角度光产生长阴影；高角度光缩短阴影。
Shadow length ≈ object height × (distance from light / light height)
阴影长度 ≈ 物体高度 × (距光源距离 / 光源高度)
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