I’ve researched the top non-slip bath mats for seniors that focus on safety, comfort, and durability. These mats feature textured surfaces, strong suction cups, drainage holes, and are made from BPA-free silicone or PVC, ensuring secure footing and easy maintenance. They’re designed to fit various bathrooms, providing extra comfort and peace of mind. If you want to know which options offer the best combination of features, keep exploring—more helpful details are ahead.
Key Takeaways
- Look for mats made from high-quality, BPA-free silicone or PVC with textured surfaces for enhanced grip and comfort.
- Ensure the mats have strong suction cups or weighted bases to stay securely in place on wet surfaces.
- Choose sizes that provide ample coverage and fit well in your bathroom to reduce trip hazards.
- Opt for easy-to-clean, quick-drying materials with drain holes to maintain hygiene and prevent mold.
- Prioritize safety certifications and anti-microbial features for reliable slip resistance and reduced bacteria growth.
Non Slip Bathtub Mat

A non-slip bathtub mat is an essential safety feature for seniors who want to enjoy bathing independently without the risk of slipping. I love how these mats are made from high-quality, BPA-free PVC, ensuring durability and safety. The 24×16-inch size fits most tubs, and you can even cut it to your preferred shape. The loofah-like textured surface offers gentle foot massage and helps remove dead skin, making it comfortable and functional. With hundreds of drain holes, water flows away quickly, preventing mold and pooling. Its stability and slip-resistant design give me peace of mind while bathing, knowing I won’t slip or fall.
Best For: seniors, children, and individuals with sensitive or painful feet seeking a safe, comfortable, and slip-resistant bathing experience.
Pros:
- Provides excellent non-slip stability on wet surfaces, enhancing safety for vulnerable users
- Made from durable, BPA-free PVC that is easy to clean and maintains its quality over time
- Loofah-like textured surface offers gentle foot massage and helps remove dead skin for added comfort
Cons:
- May feel slightly clammy or moist if not dried properly after use
- Heavier weight could require additional effort to hang or dry inside the shower or bathroom
- Slightly smaller than larger tubs, requiring trimming for custom fit in some cases
Shower Foot Scrubber Mat with Suction Cups

The Shower Foot Scrubber Mat with Suction Cups offers an easy and effective way for seniors to clean and massage their feet without bending or slipping. Made of high-quality silicone with over 500 soft bristle tips, it produces rich lather for thorough dirt and cuticle removal. Its design allows for foot exfoliation and massage, reducing strain on hips or backs. The suction cups provide a secure grip on shower surfaces, though adhesion can vary depending on wall material. It’s versatile enough to be mounted on walls or bathtubs for cleaning hard-to-reach areas. While many enjoy its benefits, some find the suction less reliable or the size small for dual-foot use.
Best For: seniors or individuals with back or hip issues seeking an easy, non-slip way to clean, exfoliate, and massage their feet in the shower or bathtub.
Pros:
- Made of high-quality, durable, quick-drying silicone with over 500 soft bristle tips for effective cleaning and massage.
- Equipped with suction cups for secure attachment to shower surfaces, reducing slip risk.
- Multi-purpose design allows use for cleaning hard-to-reach areas like the back and arms, enhancing shower convenience.
Cons:
- Suction cups may not adhere well on certain surfaces like fiberglass or smooth shower walls, affecting stability.
- The size may be too small for simultaneous use of both feet, limiting convenience.
- Bristle firmness may be insufficient for vigorous scrubbing, especially for men’s tougher feet.
TEMIR Non Slip Bath Mat with Suction Cups and Drain Holes

TEMIR Non Slip Bath Mat with Suction Cups and Drain Holes offers essential safety features that make it ideal for seniors. Its non-slip surface and strong suction cups keep the mat securely in place, reducing fall risks. Drain holes help water flow out quickly, preventing mold and keeping the mat hygienic. Designed for durability, it’s easy to clean and maintain with machine-washable materials. The cushioned support adds comfort during baths, making the experience more relaxing. Measuring 30×17 inches, it fits well inside showers and can be trimmed for a custom fit. Overall, this mat enhances bathroom safety, hygiene, and comfort effortlessly.
Best For: seniors, children, and anyone seeking a safe, hygienic, and comfortable bathing experience.
Pros:
- Non-slip surface and strong suction cups prevent slips and falls, enhancing safety.
- Drain holes ensure quick drying and reduce mold buildup, maintaining hygiene.
- Cushioned support adds comfort, making baths more relaxing for all users.
Cons:
- May require occasional reattachment of suction cups for optimal grip.
- Trimming the mat for a custom fit may be necessary, which could be cumbersome for some users.
- As a soft material, it might be less suitable for heavy-duty or very rugged environments.
Bath Mat, Ultra Thin Bathroom Rugs, No Slip, Quick Dry, Machine Washable, 15×23(17x27Inch)

Designed with safety and convenience in mind, this ultra-thin bathroom rug offers reliable slip resistance and quick drying, making it ideal for seniors who need secure footing and minimal hassle. Its 0.2-inch thickness fits smoothly under doors without getting caught in fluff, while the terry cloth material absorbs water fast and dries quickly. The rubber backing keeps the mat stable on wet floors, reducing slip risks. Easy to clean with machine wash or hand wash, it maintains its shape after multiple washes. Its simple design and neutral grey color blend seamlessly with home decor, providing a safe, comfortable, and practical solution for bathroom safety.
Best For: seniors and individuals seeking a safe, slip-resistant, quick-drying bathroom rug that fits seamlessly under doors and is easy to maintain.
Pros:
- Ultra-thin design (0.2 inches) ensures smooth door clearance and prevents entanglement.
- Non-slip rubber backing provides stability on wet floors, reducing slip hazards.
- Machine washable and durable, maintaining shape and safety features after multiple washes.
Cons:
- Slow to dry completely, taking several hours after washing.
- Not water-resistant; primarily absorbs water rather than repelling it.
- Some users experienced initial slippage, which improved after washing.
GORILLA GRIP Bath Tub Shower Mat

If you’re looking for a bath mat that offers reliable safety and stability, the Gorilla Grip Bath Tub Shower Mat is an excellent choice, especially for seniors or anyone with mobility concerns. Its patented hexagon design with pebble-textured topside feels soft on your feet while providing excellent grip. The mat measures 35×16 inches, fitting most tubs with smooth surfaces, and stays securely in place thanks to hundreds of powerful suction cups. It drains water efficiently to prevent mold and mildew and is machine washable for easy cleaning. Durable and lightweight, this mat combines safety, comfort, and convenience, making it a top-ranked option for bathroom safety.
Best For: individuals seeking a secure, non-slip bath mat for added safety, especially seniors, children, or those with mobility issues.
Pros:
- Features a patented hexagon design with pebble-textured topside for soft comfort and excellent grip.
- Equipped with hundreds of strong suction cups that securely stay in place on smooth surfaces.
- Machine washable and quick to dry, making maintenance simple and hygienic.
Cons:
- Not suitable for textured or newly refinished tubs that can’t support suction cups effectively.
- Price may vary and increase over time, potentially making it less accessible for some buyers.
- Limited color options, with popular choices mainly in blue and turquoise.
GORILLA GRIP Bath Rug Mat 30×20, Chenille Microfiber Shower Rug

The GORILLA GRIP Bath Rug Mat 30×20 stands out as an ideal choice for seniors who need reliable slip resistance and plush comfort underfoot. Crafted from nearly one inch of soft chenille microfiber, it absorbs moisture quickly while feeling warm and cozy. The durable TP Rubber backing ensures the rug stays securely in place on wet surfaces, reducing slips and falls. It’s machine washable, stain-resistant, and quick-drying, making maintenance easy. Its neutral grey color and modern design blend seamlessly with bathroom decor. Overall, this rug provides a safe, comfortable, and stylish solution that meets the needs of seniors seeking reliable non-slip bathroom accessories.
Best For: seniors and individuals seeking a plush, slip-resistant bath rug that provides safety, comfort, and easy maintenance.
Pros:
- Plush, nearly one-inch thick chenille microfiber offers superior softness and warmth underfoot
- Durable TP Rubber backing provides reliable non-slip grip on wet surfaces
- Machine washable, quick-drying, and resistant to fading and stains for easy care
Cons:
- May slide or scoot on certain surfaces if not properly secured
- The plush pile can feel less dense in some colors or with heavy use over time
- Slight initial creases from packaging may require washing to smooth out
Bath Mat, Ultra Thin Bathroom Rug, Non-Slip, Quick Dry, Machine Washable, 15×23 inches

This ultra-thin bathroom rug is perfect for seniors who need a safe, non-slip surface without sacrificing space or style. Its 0.2-inch thickness fits neatly under doors, preventing snagging, while the terry cloth material offers excellent absorbency and quick drying. The low pile design provides a secure footing, and the rubber backing keeps it stable on wet floors, reducing slip risks. Measuring 15×23 inches, it’s lightweight and versatile, suitable for bathrooms, kitchens, or laundry rooms. Easy to clean with machine wash or hand wash, it maintains durability and shape after multiple washes. This rug combines safety, practicality, and subtle style effortlessly.
Best For: seniors and individuals seeking a safe, non-slip, space-efficient bathroom rug that offers quick drying and easy maintenance.
Pros:
- Ultra-thin design fits seamlessly under doors, preventing snagging and ensuring smooth passage.
- Non-slip rubber backing provides excellent stability on wet floors, enhancing safety.
- Machine washable and durable, maintaining shape and color after multiple washes.
Cons:
- Not water resistant; designed for absorbency, not to prevent water penetration.
- Slow to dry, requiring several hours to fully air dry after washing.
- Some users may experience initial slippage, which can be mitigated by washing before use.
Rubbermaid Bath Tub and Shower Mat, 36×18 Inches

Rubbermaid’s 36×18-inch bath mat stands out as an excellent choice for seniors seeking reliable slip protection. Made of durable rubber, it features a textured surface that helps prevent slips and falls. The strong suction cups on the back keep it securely in place, even during active use. Its large size offers generous coverage, ideal for larger tubs or showers. Easy to clean—just machine wash when needed—it’s suitable for both home and commercial settings. While some users note the suction cups can lose grip over time, overall, this mat provides dependable safety, making it a smart addition to any senior’s bathing routine.
Best For: seniors and individuals seeking reliable slip prevention in bathtubs or showers for enhanced safety and confidence.
Pros:
- Durable rubber construction with textured surface for effective slip resistance
- Strong suction cups keep the mat securely in place during use
- Large size provides ample coverage for bigger tubs and showers
Cons:
- Suction cups may lose grip over time after washing
- Some users report staining or mold growth with prolonged use
- The material may deteriorate or tear with extended exposure to water and frequent cleaning
Non Slip Bathtub Mat, Anti Slip Shower Mat

If safety and stability are top priorities in your bathroom, non-slip bathtub and shower mats are an excellent choice, especially for seniors. Made from high-quality BPA-free PVC, these mats are durable, versatile, and easy to customize by cutting to fit your space. Their textured, loofah-like surface offers gentle foot massage and helps remove dead skin, while hundreds of drain holes prevent water pooling and mold. Heavyweight construction keeps the mat firmly in place, even when wet. With both sides featuring non-slip textures, these mats provide reliable stability, making your shower or bath safer and more comfortable every day.
Best For: individuals seeking a safe, comfortable, and slip-resistant solution for bathing or showering, especially seniors, children, and those with sensitive or painful feet.
Pros:
- Provides excellent anti-slip stability on wet surfaces, reducing fall risk.
- Made from durable, BPA-free PVC that is easy to clean and maintain.
- Features a textured loofah-like surface that offers gentle foot massage and exfoliation.
Cons:
- May require proper drying methods to prevent mold or mildew buildup.
- Heavier weight might necessitate hanging or additional support for drying.
- Slight clamminess can occur in humid environments if not dried thoroughly.
Bath Tub and Shower Mats, Non Slip 40 x 16 Inch

A 40 x 16-inch non-slip bath mat offers the perfect combination of safety and coverage, making it an ideal choice for seniors who need reliable footing during bath time. Its large size ensures maximum surface coverage, reducing the risk of slipping. Equipped with 362 powerful suction cups, it attaches securely to smooth, clean surfaces. The textured, pebble-like design provides a massage-like feel underfoot while enhancing grip. With 327 drain holes, water drains quickly, preventing pooling. Made of soft-touch PVC, it’s comfortable and easy to maintain—machine washable and quick-drying. This mat combines safety, comfort, and practicality for a safer bathing experience.
Best For: seniors, children, and pet owners seeking a safe, slip-resistant solution for bathtubs and showers.
Pros:
- Reliable grip with 362 large suction cups ensures secure adhesion on smooth surfaces.
- Large 40 x 16-inch size provides maximum coverage and safety.
- Textured pebble-like surface offers comfort and massage-like feel underfoot.
Cons:
- May have a slight initial odor that requires airing out.
- Needs regular cleaning and maintenance to prevent mold and mildew buildup.
- Not suitable for textured, non-smooth, or refinished bathtub surfaces for optimal adhesion.
SlipX Solutions Weighted Non Slip Bath Mat for Tub & Shower Surfaces

For seniors who need reliable grip and stability during baths or showers, the SlipX Solutions Weighted Non Slip Bath Mat offers an excellent solution. Designed specifically for textured, tiled, and porous surfaces like grout lines and pebble tile, it guarantees secure footing where others might slip. Made from soft, flexible TPE with wet-grip technology, it features hundreds of Comfort Nubs for added foot comfort. Its weighted design, 3-4 times heavier than standard mats, stays securely in place without suction cups. Easy to clean and conforming to tub shapes, this mat provides dependable safety on most textured surfaces, though it’s not recommended for smooth or refinished tubs.
Best For: seniors and individuals needing reliable grip and stability on textured, porous, or tiled bathtub and shower surfaces for enhanced safety during baths and showers.
Pros:
- Designed specifically for textured, grout-lined, and pebble tile surfaces, ensuring optimal grip and safety.
- Weighted construction (3-4x heavier than standard mats) keeps the mat securely in place without suction cups.
- Made from soft, flexible TPE with Comfort Nubs for foot comfort and easy cleaning for long-lasting hygiene.
Cons:
- Not suitable for smooth or refinished bathtub surfaces, limiting its use to textured surfaces only.
- May be less effective on very uneven or porous surfaces that are not textured or tiled.
- Slightly larger size (31” x 15”) may not fit smaller tubs or showers perfectly.
Non Slip Thin Bath Mat Bathroom Rug

The Non-Slip Thin Bath Mat Bathroom Rug is an ideal choice for seniors who prioritize safety without sacrificing space or convenience. Its ultra non-slip rubber backing grips the floor tightly, preventing slips, curling, and water leakage. The thin design, about 0.15 inches, minimizes tripping hazards and easily fits under doors, perfect for tight spaces. Made from durable polyester and rubber, it’s fade-resistant, easy to clean, and quick-drying. Its super absorbent surface quickly handles water, keeping floors dry and safe. Available in various colors, including beige, it seamlessly matches bathroom decor. This rug offers safety, practicality, and style in a compact, effective package.
Best For: seniors and individuals seeking a safe, space-saving, and easy-to-maintain bathroom rug that prevents slips and fits in tight spaces.
Pros:
- Ultra non-slip rubber backing ensures safety and prevents slipping or curling.
- Thin design (approximately 0.15 inches) fits under doors and in tight spaces, reducing tripping hazards.
- Quick-drying, super absorbent surface keeps floors dry and maintenance simple.
Cons:
- Some users find the rug thinner than expected, which may affect cushioning.
- Durability can vary; corners may bend or dirt may accumulate over time.
- Not ideal for heavy dirt or prolonged exposure to dirt and stains, requiring regular cleaning.
Better Trends 2 Piece Cotton Bath Rug Set

If you want a plush, absorbent rug set that adds warmth and style to your bathroom, the Better Trends 2 Piece Cotton Bath Rug Set is an excellent choice. Made from 100% cotton, these rugs feature a thick 15mm plush pile that feels luxurious underfoot. They’re highly absorbent (2370 GSM), easy to wash, and resist fading, shrinking, and matting. With a reversible design, you can flip them for extended use. Available in modern colors like Ivory, they blend seamlessly with various bathroom decors. While some users note slight fraying or packaging issues, overall, these rugs offer comfort, durability, and a stylish touch to your space.
Best For: those seeking a plush, highly absorbent, and stylish cotton bath rug set that adds warmth and comfort to their bathroom decor.
Pros:
- Ultra-soft, plush 15mm pile offers luxurious comfort underfoot
- Reversible design enhances durability and extended use
- Highly absorbent (2370 GSM) and resistant to fading, shrinking, and matting
Cons:
- Some users report fraying after multiple washes
- Occasional issues with batch color consistency and packaging quality
- Slight slipping on smooth surfaces for a few users
Shower Foot Scrubber Mat with Suction Cups

A shower foot scrubber mat with suction cups offers exceptional safety for seniors by providing a secure grip on wet surfaces. The strong suction cups keep the mat firmly in place, reducing the risk of slipping or falling. Its dual-purpose design combines a bath mat with exfoliating wash pads and massage bristles, promoting cleanliness and circulation without bending. Made from durable silicone and TPR, it’s lightweight, quick-drying, and easy to clean. Suitable for all shower types, including walk-ins and tubs, this mat ensures stability and comfort during every bath. It’s an effective, space-saving solution for seniors seeking safety and enhanced foot care.
Best For: seniors, individuals with limited mobility, or anyone seeking a safe, comfortable, and hygienic foot cleaning solution in the shower or bathtub.
Pros:
- Provides excellent slip resistance with strong suction cups for enhanced safety.
- Combines foot exfoliation, massage, and drainage in a space-saving, 2-in-1 design.
- Made from durable, lightweight, quick-drying materials that are easy to clean and maintain.
Cons:
- Slight size variation may occur due to manual measurement.
- Colors may appear differently on various screens, affecting visual preference.
- Suction cups may lose grip over time with frequent use or improper installation.
Granny Says Gray Bathroom Rugs (16 x 24)

Granny Says Gray Bathroom Rugs (16 x 24) stand out as an excellent choice for seniors seeking a safe and comfortable mat for their bathroom. Made from high-density microfiber, it’s super soft, plush, and absorbs water quickly, adding warmth and stress relief underfoot. The 16-by-24-inch size fits well in most bathrooms, and the 0.5-inch high pile offers extra comfort. Its non-slip TPR backing guarantees it stays put on wet floors, reducing slip risks. Easy to clean and maintain, this rug retains its softness, color, and shape wash after wash. Overall, it’s a durable, versatile option that combines safety, comfort, and style.
Best For: seniors and anyone seeking a safe, comfortable, and easy-to-maintain bathroom rug with slip-resistant features.
Pros:
- Made with high-density microfiber for softness, absorbency, and durability.
- Features non-slip TPR backing to prevent slipping on wet floors.
- Easy to clean with machine wash and tumble dry, maintaining softness and color over time.
Cons:
- Some users have reported that the non-slip backing may not be sufficient on certain surfaces.
- Size may be smaller than expected for larger bathroom spaces.
- Color discrepancies (e.g., blue vs. gray) have been noted in reviews.
Factors to Consider When Choosing a Non Slip Bath Mat for Seniors

When choosing a non-slip bath mat for seniors, I consider several key factors to guarantee safety and comfort. It’s important to look at slip resistance, size, material safety, ease of cleaning, and how durable the mat is over time. These points help me select the best option for a secure and practical bath experience.
Slip Resistance Features
Choosing a non-slip bath mat for seniors requires paying close attention to slip resistance features that guarantee safety. I look for mats with textured surfaces, like pebble or hexagon patterns, because they improve grip and reduce slipping. Secure attachment features, such as strong suction cups or weighted bases, are essential to prevent movement during use. I also favor mats with anti-slip backing made from rubber or TPR, which grip wet surfaces firmly. It’s important to verify that these slip-resistant features work well on my specific bathtub or shower, especially if the surfaces are textured or porous. Ultimately, I choose mats with drainage holes or channels that help keep the surface dry, maintaining slip resistance over time and reducing the risk of accidents.
Size and Fit
Selecting the right size for a non-slip bath mat is essential to guarantee safety and comfort. It should be large enough to cover the entire tub or shower floor, preventing slips in any zone. I recommend choosing a mat around 24×16 inches or larger, especially if mobility is limited. It’s important that the mat fits comfortably within your space without overlapping or creating trip hazards. I always check that the edges lay flat and don’t curl or bunch up during use. Additionally, consider your bathroom layout and any fixtures or accessories to ensure the mat stays securely in place. Proper sizing helps maintain stability, reduces the risk of falls, and provides a comfortable, secure footing every time you step in.
Material Safety
Ensuring your bath mat is made from safe, non-toxic materials is just as important as getting the right size. I look for mats crafted from BPA-free, hypoallergenic options like high-quality PVC or silicone to prevent skin irritation and health risks. It’s also essential that the material has anti-microbial properties or is easy to clean, reducing mold, bacteria, and mildew growth in damp environments. I prefer mats with secure, non-slip backing or suction cups made from safe, non-slip materials to prevent slipping without damaging skin or flooring. Additionally, I avoid mats with sharp edges or rough textures that could cause skin abrasions, especially for sensitive skin. Finally, I choose products that meet safety standards and certifications, ensuring reliable protection and peace of mind.
Ease of Cleaning
When it comes to maintaining a safe and hygienic bathroom environment for seniors, ease of cleaning is a crucial factor to contemplate. I recommend choosing mats made from materials like PVC or silicone, which are simple to rinse, wipe down, or even machine washable. Look for mats with drain holes or textured surfaces that prevent water from pooling, reducing mold and mildew growth. Quick-drying features are also essential, as they minimize moisture retention and make upkeep easier. It’s best to select mats that can be hung or laid flat to dry, preventing odors and extending their lifespan. Avoid mats with complex textures or sticky adhesives that trap dirt and are difficult to clean. Simplifying maintenance helps keep the bathroom safe, hygienic, and odor-free for seniors.
Durability and Longevity
A non-slip bath mat for seniors needs to be durable enough to handle frequent use and exposure to water without deteriorating. I look for mats made from high-quality materials like BPA-free PVC or silicone, which resist breaking down over time. Reinforced edges and sturdy suction cups are essential, as they prevent curling or detachment, extending the mat’s lifespan. Resistance to mold, mildew, and stains keeps the mat looking and functioning well longer. Proper maintenance, like rinsing after use and hanging it to dry, also helps prolong its life. I prioritize durability because a long-lasting mat provides consistent safety, saving me from the hassle and expense of frequent replacements. Ultimately, investing in a durable mat ensures safety and comfort for seniors over the years.
Frequently Asked Questions
How Do I Clean and Maintain Non-Slip Bath Mats Effectively?
Cleaning and maintaining my non-slip bath mats is simple. I regularly rinse them with warm water and a mild detergent to remove soap scum and dirt. I also check the grip surface for wear and replace the mat if it loses its non-slip features. To keep it fresh, I hang it to dry after each use and wash it thoroughly every few weeks. This keeps it safe and comfortable for everyday use.
Are There Specific Materials Best Suited for Senior Safety?
Thinking about safety materials is like choosing a sturdy bridge for a busy river. I’ve found that rubber and silicone are best because they’re slip-resistant and gentle on skin. These materials grip wet surfaces well, reducing falls. For seniors, I always recommend mats with textured surfaces and non-slip backing. They’re reliable and offer peace of mind, making baths safer and more comfortable.
How Often Should Non-Slip Mats Be Replaced for Optimal Safety?
I recommend replacing non-slip mats at least every 6 to 12 months, depending on usage and wear. Over time, the grip can diminish, and mold or soap buildup might compromise safety. Regularly inspect your mat for signs of wear, such as thinning or frayed edges. If you notice any slipping or damage, don’t wait—swap it promptly to ensure your safety and prevent slips in the bathroom.
Can Non-Slip Mats Prevent All Types of Slips and Falls?
Absolutely, I understand your concern about slips and falls. While non-slip mats greatly reduce the risk, they can’t prevent every accident entirely. Slips, trips, and falls can still happen due to other factors like water spills or worn-out mats. So, it’s essential to combine non-slip mats with other safety measures, like installing grab bars and keeping the bathroom dry. Prevention requires a thorough approach, not just one safety solution.
What Features Should I Look for in Mats for Elderly Individuals?
When choosing mats for elderly individuals, I look for features that prioritize safety and comfort. Non-slip backing is essential to prevent falls, while textured surfaces provide grip even when wet. I also check for cushioning to reduce impact, and verify the mats are machine washable for easy maintenance. Good drainage is important to keep the surface dry, and a non-abrasive material helps avoid skin irritation.
Conclusion
Just like a sturdy ship needs a reliable anchor, your bathroom should be equipped with a non-slip mat that keeps you steady. With the right choice, you can navigate your daily routine confidently, turning your bathroom into a safe harbor. Remember, safety isn’t just about avoiding falls but embracing peace of mind. So, pick a mat that offers both comfort and security—your personal lighthouse in the stormy seas of slippery surfaces.